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href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_ca.wikipedia.org&uselang=ca" class=""><span>Donatius</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Especial:Crea_compte&returnto=%E2%88%921&returntoquery=oldid%3D33990682" title="Us animem a crear un compte i iniciar una sessió, encara que no és obligatori" class=""><span>Crea un compte</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Especial:Registre_i_entrada&returnto=%E2%88%921&returntoquery=oldid%3D33990682" title="Us animem a registrar-vos, però no és obligatori [o]" accesskey="o" class=""><span>Inicia la sessió</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu 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mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_ca.wikipedia.org&uselang=ca"><span>Donatius</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Especial:Crea_compte&returnto=%E2%88%921&returntoquery=oldid%3D33990682" title="Us animem a crear un compte i iniciar una sessió, encara que no és obligatori"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Crea un compte</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Especial:Registre_i_entrada&returnto=%E2%88%921&returntoquery=oldid%3D33990682" title="Us animem a registrar-vos, però no és obligatori [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Inicia la sessió</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pàgines per a editors no registrats <a href="/wiki/Ajuda:Introducci%C3%B3" aria-label="Vegeu més informació sobre l'edició"><span>més informació</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Especial:Contribucions_pr%C3%B2pies" title="Una llista de les modificacions fetes des d'aquesta adreça IP [y]" accesskey="y"><span>Contribucions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Especial:Discussi%C3%B3_personal" title="Discussió sobre les edicions per aquesta adreça ip. [n]" accesskey="n"><span>Discussió per aquest IP</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Lloc"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contingut" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contingut</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mou a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">amaga</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Inici</div> </a> </li> <li id="toc-Propietats_matemàtiques" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Propietats_matemàtiques"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Propietats matemàtiques</span> </div> </a> <button aria-controls="toc-Propietats_matemàtiques-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Commuta la subsecció Propietats matemàtiques</span> </button> <ul id="toc-Propietats_matemàtiques-sublist" class="vector-toc-list"> <li id="toc-Arrels_quadrades_de_−1" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Arrels_quadrades_de_−1"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Arrels quadrades de −1</span> </div> </a> <ul id="toc-Arrels_quadrades_de_−1-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Referències" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referències"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Referències</span> </div> </a> <ul id="toc-Referències-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contingut" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Commuta la taula de continguts." > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Commuta la taula de continguts.</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">−1</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Vés a un article en una altra llengua. Disponible en 49 llengües" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-49" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">49 llengües</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/-1_(%D8%B9%D8%AF%D8%AF)" title="-1 (عدد) - àrab" lang="ar" hreflang="ar" data-title="-1 (عدد)" data-language-autonym="العربية" data-language-local-name="àrab" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E2%88%92%E0%A7%A7" title="−১ - assamès" lang="as" hreflang="as" data-title="−১" data-language-autonym="অসমীয়া" data-language-local-name="assamès" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Menos_unu" title="Menos unu - asturià" lang="ast" hreflang="ast" data-title="Menos unu" data-language-autonym="Asturianu" data-language-local-name="asturià" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/-1_(%D2%BB%D0%B0%D0%BD)" title="-1 (һан) - baixkir" lang="ba" hreflang="ba" data-title="-1 (һан)" data-language-autonym="Башҡортса" data-language-local-name="baixkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/-1" title="-1 - belarús" lang="be" hreflang="be" data-title="-1" data-language-autonym="Беларуская" data-language-local-name="belarús" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%E2%88%921_(%D0%BB%D1%96%D0%BA)" title="−1 (лік) - Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="−1 (лік)" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/-1" title="-1 - búlgar" lang="bg" hreflang="bg" data-title="-1" data-language-autonym="Български" data-language-local-name="búlgar" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E2%80%93%E0%A7%A7" title="–১ - bengalí" lang="bn" hreflang="bn" data-title="–১" data-language-autonym="বাংলা" data-language-local-name="bengalí" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%A1-_(%DA%98%D9%85%D8%A7%D8%B1%DB%95)" title="١- (ژمارە) - kurd central" lang="ckb" hreflang="ckb" data-title="١- (ژمارە)" data-language-autonym="کوردی" data-language-local-name="kurd central" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Minus_eins" title="Minus eins - alemany" lang="de" hreflang="de" data-title="Minus eins" data-language-autonym="Deutsch" data-language-local-name="alemany" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%E2%88%921" title="−1 - grec" lang="el" hreflang="el" data-title="−1" data-language-autonym="Ελληνικά" data-language-local-name="grec" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/%E2%88%921" title="−1 - anglès" lang="en" hreflang="en" data-title="−1" data-language-autonym="English" data-language-local-name="anglès" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Menos_uno" title="Menos uno - espanyol" lang="es" hreflang="es" data-title="Menos uno" data-language-autonym="Español" data-language-local-name="espanyol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/-1" title="-1 - basc" lang="eu" hreflang="eu" data-title="-1" data-language-autonym="Euskara" data-language-local-name="basc" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%E2%88%92%DB%B1" title="−۱ - persa" lang="fa" hreflang="fa" data-title="−۱" data-language-autonym="فارسی" data-language-local-name="persa" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/%E2%88%921_(luku)" title="−1 (luku) - finès" lang="fi" hreflang="fi" data-title="−1 (luku)" data-language-autonym="Suomi" data-language-local-name="finès" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/%E2%88%921_(nombre)" title="−1 (nombre) - francès" lang="fr" hreflang="fr" data-title="−1 (nombre)" data-language-autonym="Français" data-language-local-name="francès" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Ian_oner_nol" title="Ian oner nol - frisó septentrional" lang="frr" hreflang="frr" data-title="Ian oner nol" data-language-autonym="Nordfriisk" data-language-local-name="frisó septentrional" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Menos_un" title="Menos un - gallec" lang="gl" hreflang="gl" data-title="Menos un" data-language-autonym="Galego" data-language-local-name="gallec" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%E2%88%921" title="−1 - hebreu" lang="he" hreflang="he" data-title="−1" data-language-autonym="עברית" data-language-local-name="hebreu" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%E2%88%921" title="−1 - armeni" lang="hy" hreflang="hy" data-title="−1" data-language-autonym="Հայերեն" data-language-local-name="armeni" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/%E2%88%921_(angka)" title="−1 (angka) - indonesi" lang="id" hreflang="id" data-title="−1 (angka)" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesi" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-inh mw-list-item"><a href="https://inh.wikipedia.org/wiki/%E2%88%921" title="−1 - ingúix" lang="inh" hreflang="inh" data-title="−1" data-language-autonym="ГӀалгӀай" data-language-local-name="ingúix" class="interlanguage-link-target"><span>ГӀалгӀай</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/%E2%88%921" title="−1 - italià" lang="it" hreflang="it" data-title="−1" data-language-autonym="Italiano" data-language-local-name="italià" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E2%88%921" title="−1 - japonès" lang="ja" hreflang="ja" data-title="−1" data-language-autonym="日本語" data-language-local-name="japonès" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%E2%88%921" title="−1 - coreà" lang="ko" hreflang="ko" data-title="−1" data-language-autonym="한국어" data-language-local-name="coreà" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ks mw-list-item"><a href="https://ks.wikipedia.org/wiki/-1_(%DA%AF%D8%B1%D9%8E%D9%9B%D9%86%D9%9B%D8%AF)" title="-1 (گرَٛنٛد) - caixmiri" lang="ks" hreflang="ks" data-title="-1 (گرَٛنٛد)" data-language-autonym="कॉशुर / کٲشُر" data-language-local-name="caixmiri" class="interlanguage-link-target"><span>कॉशुर / کٲشُر</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Unus_negativus" title="Unus negativus - llatí" lang="la" hreflang="la" data-title="Unus negativus" data-language-autonym="Latina" data-language-local-name="llatí" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E2%88%921_(%E0%B4%B8%E0%B4%82%E0%B4%96%E0%B5%8D%E0%B4%AF)" title="−1 (സംഖ്യ) - malaiàlam" lang="ml" hreflang="ml" data-title="−1 (സംഖ്യ)" data-language-autonym="മലയാളം" data-language-local-name="malaiàlam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E2%88%92%E0%A5%A7_(%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE)" title="−१ (संख्या) - marathi" lang="mr" hreflang="mr" data-title="−१ (संख्या)" data-language-autonym="मराठी" data-language-local-name="marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/-1_(%E0%A8%B8%E0%A9%B0%E0%A8%96%E0%A8%BF%E0%A8%86)" title="-1 (ਸੰਖਿਆ) - panjabi" lang="pa" hreflang="pa" data-title="-1 (ਸੰਖਿਆ)" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="panjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/%E2%88%921" title="−1 - polonès" lang="pl" hreflang="pl" data-title="−1" data-language-autonym="Polski" data-language-local-name="polonès" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Menos_um" title="Menos um - portuguès" lang="pt" hreflang="pt" data-title="Menos um" data-language-autonym="Português" data-language-local-name="portuguès" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/%E2%88%921_(num%C4%83r)" title="−1 (număr) - romanès" lang="ro" hreflang="ro" data-title="−1 (număr)" data-language-autonym="Română" data-language-local-name="romanès" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%E2%88%921_(%D1%87%D0%B8%D1%81%D0%BB%D0%BE)" title="−1 (число) - rus" lang="ru" hreflang="ru" data-title="−1 (число)" data-language-autonym="Русский" data-language-local-name="rus" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/-1_(nummer)" title="-1 (nummer) - escocès" lang="sco" hreflang="sco" data-title="-1 (nummer)" data-language-autonym="Scots" data-language-local-name="escocès" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/%E2%88%921_(number)" title="−1 (number) - Simple English" lang="en-simple" hreflang="en-simple" data-title="−1 (number)" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/%E2%88%921_(%C5%A1tevilo)" title="−1 (število) - eslovè" lang="sl" hreflang="sl" data-title="−1 (število)" data-language-autonym="Slovenščina" data-language-local-name="eslovè" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%E2%88%921" title="−1 - serbi" lang="sr" hreflang="sr" data-title="−1" data-language-autonym="Српски / srpski" data-language-local-name="serbi" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/%E2%88%921_(tal)" title="−1 (tal) - suec" lang="sv" hreflang="sv" data-title="−1 (tal)" data-language-autonym="Svenska" data-language-local-name="suec" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/-1_(%E0%AE%8E%E0%AE%A3%E0%AF%8D)" title="-1 (எண்) - tàmil" lang="ta" hreflang="ta" data-title="-1 (எண்)" data-language-autonym="தமிழ்" data-language-local-name="tàmil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E2%88%921" title="−1 - tai" lang="th" hreflang="th" data-title="−1" data-language-autonym="ไทย" data-language-local-name="tai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%E2%88%921" title="−1 - turc" lang="tr" hreflang="tr" data-title="−1" data-language-autonym="Türkçe" data-language-local-name="turc" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/-1_(%D1%87%D0%B8%D1%81%D0%BB%D0%BE)" title="-1 (число) - ucraïnès" lang="uk" hreflang="uk" data-title="-1 (число)" data-language-autonym="Українська" data-language-local-name="ucraïnès" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/-1" title="-1 - uzbek" lang="uz" hreflang="uz" data-title="-1" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/-1" title="-1 - vietnamita" lang="vi" hreflang="vi" data-title="-1" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamita" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E2%88%921" title="−1 - xinès wu" lang="wuu" hreflang="wuu" data-title="−1" data-language-autonym="吴语" data-language-local-name="xinès wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E2%88%921" title="−1 - xinès" lang="zh" hreflang="zh" data-title="−1" data-language-autonym="中文" data-language-local-name="xinès" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/-1" title="-1 - cantonès" lang="yue" hreflang="yue" data-title="-1" data-language-autonym="粵語" data-language-local-name="cantonès" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q310395#sitelinks-wikipedia" title="Modifica enllaços interlingües" class="wbc-editpage">Modifica els enllaços</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Espais de noms"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E2%88%921" title="Vegeu el contingut de la pàgina [c]" accesskey="c"><span>Pàgina</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Discussi%C3%B3:%E2%88%921&action=edit&redlink=1" rel="discussion" class="new" title="Discussió sobre el contingut d'aquesta pàgina (encara no existeix) [t]" accesskey="t"><span>Discussió</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Canvia la variant de llengua" > <label 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title="Modifica el codi font d'aquesta pàgina [e]" accesskey="e"><span>Modifica</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E2%88%921&action=history" title="Versions antigues d'aquesta pàgina [h]" accesskey="h"><span>Mostra l'historial</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Eines de la pàgina"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Eines" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Eines</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Eines</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">mou a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">amaga</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Més opcions" > <div class="vector-menu-heading"> Accions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/%E2%88%921"><span>Mostra</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E2%88%921&action=edit" title="Modifica el codi font d'aquesta pàgina [e]" accesskey="e"><span>Modifica</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E2%88%921&action=history"><span>Mostra l'historial</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a 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class="mw-list-item"><a href="/w/index.php?title=Especial:Citau&page=%E2%88%921&id=33990682&wpFormIdentifier=titleform" title="Informació sobre com citar aquesta pàgina"><span>Citau aquest article</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Especial:UrlShortener&url=https%3A%2F%2Fca.wikipedia.org%2Fw%2Findex.php%3Ftitle%3D%25E2%2588%25921%26oldid%3D33990682"><span>Obtén una URL abreujada</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Especial:QrCode&url=https%3A%2F%2Fca.wikipedia.org%2Fw%2Findex.php%3Ftitle%3D%25E2%2588%25921%26oldid%3D33990682"><span>Descarrega el codi QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Imprimeix/exporta </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a 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wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q310395" title="Enllaç a l'element del repositori de dades connectat [g]" accesskey="g"><span>Element a Wikidata</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Eines de la pàgina"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Aparença"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Aparença</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mou a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">amaga</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">De la Viquipèdia, l'enciclopèdia lliure</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><div class="cdx-message cdx-message--block cdx-message--warning mw-revision"><span 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Pot tenir inexactituds o contingut no apropiat no present en la <span class="plainlinks"><a class="external text" href="https://ca.wikipedia.org/wiki/%E2%88%921">versió actual</a></span>.</div><div id="mw-revision-nav">(<a href="/w/index.php?title=%E2%88%921&diff=prev&oldid=33990682" title="−1">dif.</a>) <a href="/w/index.php?title=%E2%88%921&direction=prev&oldid=33990682" title="−1">←la pròxima versió més antiga</a> | vegeu la versió actual (dif.) | Versió més nova → (dif.)</div></div></div></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="ca" dir="ltr"><table class="plainlinks ambox ambox-content" style="" data-severity="2"> <tbody><tr> <td class="mbox-image" style="width: 52px;"> <span typeof="mw:File"><a href="/wiki/Fitxer:Crystal128-pipe.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Crystal128-pipe.svg/25px-Crystal128-pipe.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Crystal128-pipe.svg/38px-Crystal128-pipe.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Crystal128-pipe.svg/50px-Crystal128-pipe.svg.png 2x" data-file-width="192" data-file-height="192" /></a></span></td> <td class="mbox-text" style=""> <div class="mbox-text-span">Aquest article o secció no <a href="/wiki/Viquip%C3%A8dia:Citau_les_fonts" title="Viquipèdia:Citau les fonts">cita les fonts</a> o necessita més referències per a la seva <a href="/wiki/VP:VER" class="mw-redirect" title="VP:VER">verificabilitat</a>.</div> </td> </tr> </tbody></table> <style data-mw-deduplicate="TemplateStyles:r34261971">.mw-parser-output .hatnote{width:100%;border-color:#77ccff;color:var(--color-base,#202122);background-color:#f5f5f5;margin-bottom:1em;font-style:italic}.mw-parser-output .hatnote i{font-style:normal}@media screen{html.skin-theme-clientpref-night .mw-parser-output .hatnote{color:var(--color-inverted,#fff);background-color:var(--background-color-inverted,#101418)}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .hatnote{color:var(--color-inverted,#fff);background-color:var(--background-color-inverted,#101418)}}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style> <table class="hatnote" cellspacing="5"> <tbody><tr> <td style="width: 25px; vertical-align: top;"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Disambig_grey.svg/22px-Disambig_grey.svg.png" decoding="async" width="22" height="17" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Disambig_grey.svg/33px-Disambig_grey.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Disambig_grey.svg/44px-Disambig_grey.svg.png 2x" data-file-width="260" data-file-height="200" /></span></span> </td> <td>Aquest article tracta sobre el nombre. Vegeu-ne altres significats a «<a href="/wiki/1_aC" title="1 aC">1 aC</a>». </td></tr></tbody></table> <table class="infobox" style="font-size:90%;width:25em"><caption style="font-weight:bold;background:#b0d1ad;"><span style="float:left;"><span typeof="mw:File"><span title="Infotaula nombre"><img alt="Infotaula nombre" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Emojione_BW_0037.svg/22px-Emojione_BW_0037.svg.png" decoding="async" width="22" height="22" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Emojione_BW_0037.svg/33px-Emojione_BW_0037.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Emojione_BW_0037.svg/44px-Emojione_BW_0037.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span></span>−1</caption><tbody><tr><td colspan="2" class="infobox-full-data infobox-data" style="text-align:center"><span typeof="mw:File"><a href="/w/index.php?title=Fitxer:Ic_exposure_minus_1_48px.svg&lang=ca" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Ic_exposure_minus_1_48px.svg/langca-300px-Ic_exposure_minus_1_48px.svg.png" decoding="async" width="300" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Ic_exposure_minus_1_48px.svg/langca-450px-Ic_exposure_minus_1_48px.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Ic_exposure_minus_1_48px.svg/langca-600px-Ic_exposure_minus_1_48px.svg.png 2x" data-file-width="48" data-file-height="48" /></a></span></td></tr><tr><th scope="row" class="infobox-label" style="text-align:left;width:35%; background:#eeeeee;">Tipus</th><td class="infobox-data"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q18659417" class="extiw" title="d:Special:EntityPage/Q18659417">enter negatiu</a>, <a href="/wiki/Nombre_enter" title="Nombre enter">nombre enter</a> i <a href="/wiki/Nombre_senar" title="Nombre senar">nombre senar</a> <span class="penicon"><span class="mw-valign-baseline" typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q310395?uselang=ca#P31" title="Modifica el valor a Wikidata"><img alt="Modifica el valor a Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/10px-Arbcom_ru_editing.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/15px-Arbcom_ru_editing.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/20px-Arbcom_ru_editing.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></span></td></tr><tr><th colspan="2" class="infobox-header" style="text-align:center;background:#b0d1ad;">Propietats</th></tr><tr><th scope="row" class="infobox-label" style="text-align:left;width:35%; background:#eeeeee;">Valor</th><td class="infobox-data">−1 <span class="penicon"><span class="mw-valign-baseline" typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q310395?uselang=ca#P1181" title="Modifica el valor a Wikidata"><img alt="Modifica el valor a Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/10px-Arbcom_ru_editing.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/15px-Arbcom_ru_editing.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/20px-Arbcom_ru_editing.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></span></td></tr><tr><th colspan="2" class="infobox-header" style="text-align:center;background:#b0d1ad;">Altres numeracions</th></tr><tr><th colspan="2" class="infobox-header" style="text-align:center;background:#b0d1ad;">Fórmules</th></tr><tr><td colspan="2" style="text-align:center;background:#b0d1ad;">10px <span class="penicon"><span class="mw-valign-baseline" typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q310395?uselang=ca#P31" title="Modifica el valor a Wikidata"><img alt="Modifica el valor a Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/10px-Arbcom_ru_editing.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/15px-Arbcom_ru_editing.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/20px-Arbcom_ru_editing.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></span></td></tr></tbody></table> <p>En <a href="/wiki/Matem%C3%A0tiques" title="Matemàtiques">matemàtiques</a>, <b>−1</b> (<b>menys u</b>) és un <a href="/wiki/Nombre_enter" title="Nombre enter">nombre enter</a> <a href="/wiki/Negatiu" title="Negatiu">negatiu</a>, que va entre <a href="/wiki/Nombre_-2" class="mw-redirect" title="Nombre -2">menys dos</a> (-2) i <a href="/wiki/Zero" title="Zero">zero</a> (0). La seva <a href="/wiki/Representaci%C3%B3_bin%C3%A0ria" class="mw-redirect" title="Representació binària">representació binària</a> pot ser −1 o 11...11 (en funció del format i del nombre de bits utilitzats per a representar nombres enters), la <a href="/wiki/Representaci%C3%B3_octal" class="mw-redirect" title="Representació octal">representació octal</a> pot ser −1 o 77..77 (ídem) i l'<a href="/wiki/Representaci%C3%B3_hexadecimal" class="mw-redirect" title="Representació hexadecimal">hexadecimal</a> pot ser −1 o FF..FF (ídem). La seva <a href="/wiki/Factoritzaci%C3%B3_en_nombres_primers" class="mw-redirect" title="Factorització en nombres primers">factorització en nombres primers</a> és 1 × −1 = −1. És l'<a href="/wiki/Additiu_invers" class="mw-redirect" title="Additiu invers">additiu invers</a> d'<a href="/wiki/U_(nombre)" title="U (nombre)">1</a>, és a dir, el nombre que, en sumar-li 1, dona 0. També forma part de la famosa <a href="/wiki/Identitat_d%27Euler" title="Identitat d'Euler">identitat d'Euler</a>: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e^{i\pi }=-1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>π</mi> </mrow> </msup> <mo>=</mo> <mo>−</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e^{i\pi }=-1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00ba628c5431f37a0be483c26111b1078c036f6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:8.894ex; height:2.843ex;" alt="{\displaystyle e^{i\pi }=-1}"></span> </p><p>Els negatius tenen algunes propietats similars però lleugerament diferents a les propietats dels nombres enters positius. Els negatius serien un multiplicador d'identitat si no fos pel canvi de signe: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (-1)\cdot x=-x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (-1)\cdot x=-x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a43eefbabc93e5f9095a22d9e5b661d362600d37" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.025ex; height:2.843ex;" alt="{\displaystyle (-1)\cdot x=-x}"></span></dd></dl> <p>L'<a href="/wiki/Arrel_quadrada" title="Arrel quadrada">arrel quadrada</a> d'un nombre negatiu N és la mateixa que la del nombre positiu però en el pla <a href="/wiki/Complex" class="mw-redirect" title="Complex">complex</a>. És a dir: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {-N}}={\sqrt {N\cdot -1}}={\sqrt {N}}\cdot i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo>−</mo> <mi>N</mi> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>N</mi> <mo>⋅</mo> <mo>−</mo> <mn>1</mn> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>N</mi> </msqrt> </mrow> <mo>⋅</mo> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {-N}}={\sqrt {N\cdot -1}}={\sqrt {N}}\cdot i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de638690d5c0faa8222fe34b010e2defeda360f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.135ex; height:3.176ex;" alt="{\displaystyle {\sqrt {-N}}={\sqrt {N\cdot -1}}={\sqrt {N}}\cdot i}"></span></dd></dl> <p>En <a href="/wiki/Inform%C3%A0tica" title="Informàtica">informàtica</a>, <b>−1</b> de vegades és usat en alguns llenguatges de programació per a representar un valor inicial per a enters i també es pot utilitzar per a inicialitzar una variable que no conté cap informació útil si, per exemple, s'està cercant un valor d'una llista de nombres positius. </p><p>Ocurrències del nombre menys u: </p> <ul><li>Designa l'any <a href="/wiki/2_aC" title="2 aC">2 aC</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Propietats_matemàtiques"><span id="Propietats_matem.C3.A0tiques"></span>Propietats matemàtiques</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E2%88%921&action=edit&section=1" title="Modifica la secció: Propietats matemàtiques"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>És l'<a href="/wiki/Oposat_(matem%C3%A0tiques)" title="Oposat (matemàtiques)">invers de l'addició</a> del nombre <a href="/wiki/U_(nombre)" title="U (nombre)">1</a>, és a dir, el nombre que, quan se li suma a 1, dona 0.</li> <li>Té algunes propietats simliars però lleugerament differents a les propietats positives (de l'<a href="/w/index.php?title=U_(nombre)u&action=edit&redlink=1" class="new" title="U (nombre)u (encara no existeix)">U (nombre)u</a>); seria un multiplicador d'identitat si no fos per un canvi de signe: (−1) · x = −x.</li> <li>En el context de <a href="/wiki/Nombre_imaginari" title="Nombre imaginari">nombres imaginaris</a>, i^2 és igual a −1, on i és la unitat imaginària.</li> <li>El nombre −1 està present en la <a href="/wiki/Identitat_d%27Euler" title="Identitat d'Euler">identitat d'Euler</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e^{i\pi }=-1\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>π</mi> </mrow> </msup> <mo>=</mo> <mo>−</mo> <mn>1</mn> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e^{i\pi }=-1\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0b769e6691082cd67067e41beab7887e4284355" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; margin-right: -0.387ex; width:9.281ex; height:2.843ex;" alt="{\displaystyle e^{i\pi }=-1\,\!}"></span>.</li> <li>És, en <a href="/wiki/Inform%C3%A0tica" title="Informàtica">informàtica</a>, un valor inicial per a enters en alguns llenguatges; també s'utilitza per mostrar una variable que no conté cap informació útil.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Arrels_quadrades_de_−1"><span id="Arrels_quadrades_de_.E2.88.921"></span>Arrels quadrades de −1</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E2%88%921&action=edit&section=2" title="Modifica la secció: Arrels quadrades de −1"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Tot i que no hi ha cap arrel quadrada <a href="/wiki/Nombre_real" title="Nombre real">real</a> de −1, el <a href="/wiki/Nombre_complex" title="Nombre complex">nombre complex</a> <span class="texhtml"><var><a href="/wiki/Unitat_imagin%C3%A0ria" title="Unitat imaginària">i</a></var></span> satisfà <span class="texhtml"><i>i</i><sup>2</sup> = −1</span>, i com a tal es pot considerar una <a href="/wiki/Arrel_quadrada" title="Arrel quadrada">arrel quadrada</a> de −1.<sup id="cite_ref-imaginary_1-0" class="reference"><a href="#cite_note-imaginary-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> L'únic altre nombre complex el quadrat del qual és −1 és −<span class="texhtml"><var>i</var></span> ja que tot nombre complex diferent de zero té exactament dues arrels quadrades, tal com estableix el <a href="/wiki/Teorema_fonamental_de_l%27%C3%A0lgebra" title="Teorema fonamental de l'àlgebra">teorema fonamental de l'àlgebra</a>. En l'àlgebra dels <a href="/wiki/Quaterni%C3%B3" title="Quaternió">quaternions</a> – on el teorema fonamental no aplica – que conté els nombres complexos, l'equació <span class="texhtml"><i>x</i><sup>2</sup> = −1</span> té infinites solucions.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Referències"><span id="Refer.C3.A8ncies"></span>Referències</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E2%88%921&action=edit&section=3" title="Modifica la secció: Referències"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist {{#if: | references-column-count references-column-count-{{{col}}}" style="list-style-type: decimal;"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-imaginary-1"><span class="mw-cite-backlink"><a href="#cite_ref-imaginary_1-0">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFBauer2007"><span style="font-variant: small-caps;">Bauer</span>, Cameron. «Chapter 13: Complex Numbers». A: <i>Algebra for Athletes</i>. 2nd.  Hauppauge: <a href="/w/index.php?title=Nova_Science_Publishers&action=edit&redlink=1" class="new" title="Nova Science Publishers (encara no existeix)">Nova Science Publishers</a>, 2007, p. 273. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/978-1-60021-925-2" title="Especial:Fonts bibliogràfiques/978-1-60021-925-2">ISBN 978-1-60021-925-2</a></span>. <span style="font-size:90%;"><a href="/wiki/OCLC" class="mw-redirect" title="OCLC">OCLC</a> <a rel="nofollow" class="external text" href="http://worldcat.org/oclc/957126114">957126114</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Algebra+for+Athletes&rft.atitle=Chapter+13%3A+Complex+Numbers&rft.aulast=Bauer&rft.aufirst=Cameron&rft.date=2007&rft.edition=2nd&rft.pub=%5B%5BNova+Science+Publishers%5D%5D&rft.place=Hauppauge&rft.pages=273&rft.isbn=978-1-60021-925-2&rft_id=info:oclcnum/957126114"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFPerlis1971"><span style="font-variant: small-caps;">Perlis</span>, Sam. «Capsule 77: Quaternions». A: <i>Historical Topics in Algebra</i>. 31.  Reston, VA: <a href="/w/index.php?title=National_Council_of_Teachers_of_Mathematics&action=edit&redlink=1" class="new" title="National Council of Teachers of Mathematics (encara no existeix)">National Council of Teachers of Mathematics</a>, 1971, p. 39 (Historical Topics for the Mathematical Classroom). <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/9780873530583" title="Especial:Fonts bibliogràfiques/9780873530583">ISBN 9780873530583</a></span>. <span style="font-size:90%;"><a href="/wiki/OCLC" class="mw-redirect" title="OCLC">OCLC</a> <a rel="nofollow" class="external text" href="http://worldcat.org/oclc/195566">195566</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Historical+Topics+in+Algebra&rft.atitle=Capsule+77%3A+Quaternions&rft.aulast=Perlis&rft.aufirst=Sam&rft.date=1971&rft.pub=%5B%5BNational+Council+of+Teachers+of+Mathematics%5D%5D&rft.place=Reston%2C+VA&rft.pages=39&rft.series=Historical+Topics+for+the+Mathematical+Classroom&rft.isbn=9780873530583&rft_id=info:oclcnum/195566"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFPorteous1995"><span style="font-variant: small-caps;">Porteous</span>, Ian R. «Chapter 8: Quaternions». A: <a rel="nofollow" class="external text" href="https://www.maths.ed.ac.uk/~v1ranick/papers/porteous3.pdf"><i>Clifford Algebras and the Classical Groups</i></a>. 50.  Cambridge: <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>, 1995, p. 60 (Cambridge Studies in Advanced Mathematics). <span style="font-size:90%;"><a href="/wiki/DOI" title="DOI">DOI</a> <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1017/CBO9780511470912.009">10.1017/CBO9780511470912.009</a></span>. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/9780521551779" title="Especial:Fonts bibliogràfiques/9780521551779">ISBN 9780521551779</a></span>. <span style="font-size:90%;"><a href="/wiki/OCLC" class="mw-redirect" title="OCLC">OCLC</a> <a rel="nofollow" class="external text" href="http://worldcat.org/oclc/32348823">32348823</a></span>.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Clifford+Algebras+and+the+Classical+Groups&rft.atitle=Chapter+8%3A+Quaternions&rft.aulast=Porteous&rft.aufirst=Ian+R.&rft.date=1995&rft.pub=%5B%5BCambridge+University+Press%5D%5D&rft.place=Cambridge&rft.pages=60&rft.series=Cambridge+Studies+in+Advanced+Mathematics&rft.isbn=9780521551779&rft_id=info:oclcnum/32348823&rft_id=info:doi/10.1017%2FCBO9780511470912.009&rft_id=https%3A%2F%2Fwww.maths.ed.ac.uk%2F%7Ev1ranick%2Fpapers%2Fporteous3.pdf"><span style="display: none;"> </span></span></span> </li> </ol></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Obtingut de «<a dir="ltr" href="https://ca.wikipedia.org/w/index.php?title=−1&oldid=33990682">https://ca.wikipedia.org/w/index.php?title=−1&oldid=33990682</a>»</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Especial:Categorias" title="Especial:Categorias">Categoria</a>: <ul><li><a href="/wiki/Categoria:Nombres_enters" title="Categoria:Nombres enters">Nombres enters</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Categoria oculta: <ul><li><a href="/wiki/Categoria:Articles_sense_refer%C3%A8ncies" title="Categoria:Articles sense referències">Articles sense referències</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> La pàgina va ser modificada per darrera vegada el 22 set 2024 a les 20:21.</li> <li id="footer-info-copyright">El text està disponible sota la <a href="/wiki/Viquip%C3%A8dia:Text_de_la_llic%C3%A8ncia_de_Creative_Commons_Reconeixement-Compartir_Igual_4.0_No_adaptada" title="Viquipèdia:Text de la llicència de Creative Commons Reconeixement-Compartir Igual 4.0 No adaptada"> Llicència de Creative Commons Reconeixement i Compartir-Igual</a>; es poden aplicar termes addicionals. 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