{"id":9152,"date":"2012-05-20T21:26:26","date_gmt":"2012-05-20T20:26:26","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=9152"},"modified":"2021-12-29T02:42:44","modified_gmt":"2021-12-29T02:42:44","slug":"represente-na-forma-algebrica-os-numeros-complexos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=9152","title":{"rendered":"Represente na forma alg\u00e9brica os n\u00fameros complexos"},"content":{"rendered":"<p><ul id='GTTabs_ul_9152' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_9152' class='GTTabs_curr'><a  id=\"9152_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_9152' ><a  id=\"9152_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_9152'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Represente na forma alg\u00e9brica os n\u00fameros complexos:<\/p>\n<ol>\n<li>$z = 5\\operatorname{cis} \\pi $<\/li>\n<li>$z = 3\\operatorname{cis} \\frac{\\pi }{2}$<\/li>\n<li>$z = \\sqrt 2 \\operatorname{cis} \\frac{{7\\pi }}{4}$<\/li>\n<li>$z = \\operatorname{cis} \\frac{{7\\pi }}{6}$<\/li>\n<li>$z = \\sqrt 3 \\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_9152' onClick='GTTabs_show(1,9152)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_9152'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{5\\operatorname{cis} \\pi } \\\\<br \/>\n{}&amp; = &amp;{5\\left( {\\cos \\pi\u00a0 + i\\operatorname{sen} \\pi } \\right)} \\\\<br \/>\n{}&amp; = &amp;{5\\left( { &#8211; 1 + 0i} \\right)} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; 5}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{3\\operatorname{cis} \\frac{\\pi }{2}} \\\\<br \/>\n{}&amp; = &amp;{3\\left( {\\cos \\frac{\\pi }{2} + i\\operatorname{sen} \\frac{\\pi }{2}} \\right)} \\\\<br \/>\n{}&amp; = &amp;{3\\left( {0 + i} \\right)} \\\\<br \/>\n{}&amp; = &amp;{3i}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{\\sqrt 2 \\operatorname{cis} \\frac{{7\\pi }}{4}} \\\\<br \/>\n{}&amp; = &amp;{\\sqrt 2 \\left( {\\cos \\frac{{7\\pi }}{4} + i\\operatorname{sen} \\frac{{7\\pi }}{4}} \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\sqrt 2 \\left( {\\cos \\frac{\\pi }{4} + i\\operatorname{sen} \\left( { &#8211; \\frac{\\pi }{4}} \\right)} \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\sqrt 2 \\left( {\\frac{{\\sqrt 2 }}{2} &#8211; \\frac{{\\sqrt 2 }}{2}i} \\right)} \\\\<br \/>\n{}&amp; = &amp;{1 &#8211; i}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{\\operatorname{cis} \\frac{{7\\pi }}{4}} \\\\<br \/>\n{}&amp; = &amp;{\\cos \\frac{{7\\pi }}{6} + i\\operatorname{sen} \\frac{{7\\pi }}{6}} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; \\cos \\frac{\\pi }{6} &#8211; i\\operatorname{sen} \\frac{\\pi }{6}} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; \\frac{{\\sqrt 3 }}{2} &#8211; \\frac{1}{2}i}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{\\sqrt 3 \\operatorname{cis} \\left( { &#8211; \\frac{\\pi }{3}} \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\sqrt 3 \\left( {\\cos \\left( { &#8211; \\frac{\\pi }{3}} \\right) + i\\operatorname{sen} \\left( { &#8211; \\frac{\\pi }{3}} \\right)} \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\sqrt 3 \\left( {\\cos \\frac{\\pi }{3} &#8211; i\\operatorname{sen} \\frac{\\pi }{3}} \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\sqrt 3 \\left( {\\frac{1}{2} &#8211; \\frac{{\\sqrt 3 }}{2}i} \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{\\sqrt 3 }}{2} &#8211; \\frac{3}{2}i}<br \/>\n\\end{array}$$<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_9152' onClick='GTTabs_show(0,9152)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Represente na forma alg\u00e9brica os n\u00fameros complexos: $z = 5\\operatorname{cis} \\pi $ $z = 3\\operatorname{cis} \\frac{\\pi }{2}$ $z = \\sqrt 2 \\operatorname{cis} \\frac{{7\\pi }}{4}$ $z = \\operatorname{cis} \\frac{{7\\pi }}{6}$ $z =&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19547,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,310],"tags":[427,315,314,18],"series":[],"class_list":["post-9152","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-forma-algebrica","tag-forma-trigonometrica","tag-numeros-complexos"],"views":1451,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat166.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9152","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=9152"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9152\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19547"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9152"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9152"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9152"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=9152"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}