{"id":9157,"date":"2012-05-20T21:51:42","date_gmt":"2012-05-20T20:51:42","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=9157"},"modified":"2021-12-29T02:46:38","modified_gmt":"2021-12-29T02:46:38","slug":"represente-na-forma-trigonometrica-os-conjugados-dos-numeros-complexos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=9157","title":{"rendered":"Represente, na forma trigonom\u00e9trica, os conjugados dos n\u00fameros complexos"},"content":{"rendered":"<p><ul id='GTTabs_ul_9157' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_9157' class='GTTabs_curr'><a  id=\"9157_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_9157' ><a  id=\"9157_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_9157'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Represente, na forma trigonom\u00e9trica, os conjugados dos n\u00fameros complexos:<\/p>\n<ol>\n<li>$z =\u00a0 &#8211; 3$<\/li>\n<li>$z = 2i$<\/li>\n<li>$z = 2\\operatorname{cis} \\left( { &#8211; \\frac{\\pi }{3}} \\right)$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_9157' onClick='GTTabs_show(1,9157)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_9157'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p><strong>Forma trigonom\u00e9trica do conjugado<\/strong>:<\/p>\n<p style=\"text-align: center;\">Se $z = \\rho \\operatorname{cis} \\theta $, ent\u00e3o $\\overline z\u00a0 = \\rho \\operatorname{cis} \\left( { &#8211; \\theta } \\right)$.<br \/>\n\u00ad<\/p>\n<\/blockquote>\n<ol>\n<li>Como $z =\u00a0 &#8211; 3 = 3\\operatorname{cis} \\pi $, ent\u00e3o $\\overline z\u00a0 = 3\\operatorname{cis} \\left( { &#8211; \\pi } \\right)$.<br \/>\n\u00ad<\/li>\n<li>Como $z = 2i = 2\\operatorname{cis} \\frac{\\pi }{2}$, ent\u00e3o $\\overline z\u00a0 = 2\\operatorname{cis} \\left( { &#8211; \\frac{\\pi }{2}} \\right)$.<br \/>\n\u00ad<\/li>\n<li>Como $z = 2\\operatorname{cis} \\left( { &#8211; \\frac{\\pi }{3}} \\right)$, ent\u00e3o $\\overline z\u00a0 = 2\\operatorname{cis} \\frac{\\pi }{3}$.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_9157' onClick='GTTabs_show(0,9157)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Represente, na forma trigonom\u00e9trica, os conjugados dos n\u00fameros complexos: $z =\u00a0 &#8211; 3$ $z = 2i$ $z = 2\\operatorname{cis} \\left( { &#8211; \\frac{\\pi }{3}} \\right)$ Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":19564,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,310],"tags":[427,312,314,18],"series":[],"class_list":["post-9157","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-12--ano","category-aplicando","category-numeros-complexos-12--ano","tag-12-o-ano","tag-conjugado","tag-forma-trigonometrica","tag-numeros-complexos"],"views":2783,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat183.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9157","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=9157"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9157\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9157"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9157"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9157"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=9157"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}