{"id":9212,"date":"2012-05-21T18:51:15","date_gmt":"2012-05-21T17:51:15","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=9212"},"modified":"2021-12-29T13:36:05","modified_gmt":"2021-12-29T13:36:05","slug":"escreva-z-na-forma-algebrica","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=9212","title":{"rendered":"Escreva $z$ na forma alg\u00e9brica"},"content":{"rendered":"<p><ul id='GTTabs_ul_9212' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_9212' class='GTTabs_curr'><a  id=\"9212_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_9212' ><a  id=\"9212_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_9212'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Escreva $z$ na forma alg\u00e9brica:<\/p>\n<ol>\n<li>$z = \\operatorname{cis} \\frac{\\pi }{3}$<\/li>\n<li>$z = 2\\operatorname{cis} \\left( { &#8211; \\frac{\\pi }{3}} \\right)$<\/li>\n<li>$z = \\sqrt 3 \\operatorname{cis} \\left( { &#8211; \\frac{{5\\pi }}{6}} \\right)$<\/li>\n<li>$z = 2\\operatorname{cis} \\left( {\\frac{{3\\pi }}{4}} \\right)$<\/li>\n<li>$z = \\operatorname{cis} \\frac{{9\\pi }}{2}$<\/li>\n<li>$z = 9\\operatorname{cis} 2\\pi $<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_9212' onClick='GTTabs_show(1,9212)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_9212'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{\\operatorname{cis} \\frac{\\pi }{3}} \\\\<br \/>\n{}&amp; = &amp;{\\cos \\frac{\\pi }{3} + i\\operatorname{sen} \\frac{\\pi }{3}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{1}{2} + \\frac{{\\sqrt 3 }}{2}i}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{2\\operatorname{cis} \\left( { &#8211; \\frac{\\pi }{3}} \\right)} \\\\<br \/>\n{}&amp; = &amp;{2\\left( {\\cos \\left( { &#8211; \\frac{\\pi }{3}} \\right) + i\\operatorname{sen} \\left( { &#8211; \\frac{\\pi }{3}} \\right)} \\right)} \\\\<br \/>\n{}&amp; = &amp;{2\\left( {\\cos \\frac{\\pi }{3} &#8211; i\\operatorname{sen} \\frac{\\pi }{3}} \\right)} \\\\<br \/>\n{}&amp; = &amp;{2\\left( {\\frac{1}{2} &#8211; \\frac{{\\sqrt 3 }}{2}i} \\right)} \\\\<br \/>\n{}&amp; = &amp;{1 &#8211; \\sqrt 3 i}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{\\sqrt 3 \\operatorname{cis} \\left( { &#8211; \\frac{{5\\pi }}{6}} \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\sqrt 3 \\left( {\\cos \\left( { &#8211; \\frac{{5\\pi }}{6}} \\right) + i\\operatorname{sen} \\left( { &#8211; \\frac{{5\\pi }}{6}} \\right)} \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\sqrt 3 \\left( { &#8211; \\cos \\frac{\\pi }{6} &#8211; i\\operatorname{sen} \\frac{\\pi }{6}} \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\sqrt 3 \\left( { &#8211; \\frac{{\\sqrt 3 }}{2} &#8211; \\frac{1}{2}i} \\right)} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; \\frac{3}{2} &#8211; \\frac{{\\sqrt 3 }}{2}i}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{2\\operatorname{cis} \\left( {\\frac{{3\\pi }}{4}} \\right)} \\\\<br \/>\n{}&amp; = &amp;{2\\left( {\\cos \\left( {\\frac{{3\\pi }}{4}} \\right) + i\\operatorname{sen} \\left( {\\frac{{3\\pi }}{4}} \\right)} \\right)} \\\\<br \/>\n{}&amp; = &amp;{2\\left( { &#8211; \\frac{{\\sqrt 2 }}{2} + i\\frac{{\\sqrt 2 }}{2}} \\right)} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; \\sqrt 2\u00a0 + \\sqrt 2 i}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{\\operatorname{cis} \\frac{{9\\pi }}{2}} \\\\<br \/>\n{}&amp; = &amp;{\\cos \\frac{{9\\pi }}{2} + i\\operatorname{sen} \\frac{{9\\pi }}{2}} \\\\<br \/>\n{}&amp; = &amp;{\\cos \\frac{\\pi }{2} + i\\operatorname{sen} \\frac{\\pi }{2}} \\\\<br \/>\n{}&amp; = &amp;i<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{9\\operatorname{cis} 2\\pi } \\\\<br \/>\n{}&amp; = &amp;{9\\left( {\\cos 2\\pi\u00a0 + i\\operatorname{sen} 2\\pi } \\right)} \\\\<br \/>\n{}&amp; = &amp;9<br \/>\n\\end{array}$$<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_9212' onClick='GTTabs_show(0,9212)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Escreva $z$ na forma alg\u00e9brica: $z = \\operatorname{cis} \\frac{\\pi }{3}$ $z = 2\\operatorname{cis} \\left( { &#8211; \\frac{\\pi }{3}} \\right)$ $z = \\sqrt 3 \\operatorname{cis} \\left( { &#8211; \\frac{{5\\pi }}{6}} \\right)$ $z&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14113,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,310],"tags":[427,315,18],"series":[],"class_list":["post-9212","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-numeros-complexos"],"views":2151,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat55.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9212","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=9212"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9212\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14113"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9212"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9212"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9212"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=9212"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}