{"id":9203,"date":"2012-05-21T17:45:43","date_gmt":"2012-05-21T16:45:43","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=9203"},"modified":"2021-12-29T13:25:28","modified_gmt":"2021-12-29T13:25:28","slug":"determine-na-forma-trigonometrica","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=9203","title":{"rendered":"Determine na forma trigonom\u00e9trica"},"content":{"rendered":"<p><ul id='GTTabs_ul_9203' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_9203' class='GTTabs_curr'><a  id=\"9203_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_9203' ><a  id=\"9203_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_9203'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Sendo $$\\begin{array}{*{20}{c}}<br \/>\n{z = 2\\operatorname{cis} \\frac{\\pi }{3}}&amp;{\\text{e}}&amp;{w = 3\\operatorname{cis} \\frac{\\pi }{2}}<br \/>\n\\end{array}$$ determine na forma trigonom\u00e9trica:<\/p>\n<ol>\n<li>$zw$<\/li>\n<li>$\\frac{z}{w}$<\/li>\n<li>${z^3}$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_9203' onClick='GTTabs_show(1,9203)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_9203'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>$$\\begin{array}{*{20}{c}}<br \/>\n{z = 2\\operatorname{cis} \\frac{\\pi }{3}}&amp;{\\text{e}}&amp;{w = 3\\operatorname{cis} \\frac{\\pi }{2}}<br \/>\n\\end{array}$$<\/p>\n<\/blockquote>\n<ol>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{zw}&amp; = &amp;{\\left( {2\\operatorname{cis} \\frac{\\pi }{3}} \\right) \\times \\left( {3\\operatorname{cis} \\frac{\\pi }{2}} \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\left( {2 \\times 3} \\right)\\operatorname{cis} \\left( {\\frac{\\pi }{3} + \\frac{\\pi }{2}} \\right)} \\\\<br \/>\n{}&amp; = &amp;{6\\operatorname{cis} \\frac{{5\\pi }}{6}}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{\\frac{z}{w}}&amp; = &amp;{\\frac{{2\\operatorname{cis} \\frac{\\pi }{3}}}{{3\\operatorname{cis} \\frac{\\pi }{2}}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{2}{3}\\operatorname{cis} \\left( {\\frac{\\pi }{3} &#8211; \\frac{\\pi }{2}} \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\frac{2}{3}\\operatorname{cis} \\left( { &#8211; \\frac{\\pi }{6}} \\right)}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{{z^3}}&amp; = &amp;{{{\\left( {2\\operatorname{cis} \\frac{\\pi }{3}} \\right)}^3}} \\\\<br \/>\n{}&amp; = &amp;{{2^3}\\operatorname{cis} \\left( {3 \\times \\frac{\\pi }{3}} \\right)} \\\\<br \/>\n{}&amp; = &amp;{8\\operatorname{cis} \\pi }<br \/>\n\\end{array}$$<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_9203' onClick='GTTabs_show(0,9203)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Sendo $$\\begin{array}{*{20}{c}} {z = 2\\operatorname{cis} \\frac{\\pi }{3}}&amp;{\\text{e}}&amp;{w = 3\\operatorname{cis} \\frac{\\pi }{2}} \\end{array}$$ determine na forma trigonom\u00e9trica: $zw$ $\\frac{z}{w}$ ${z^3}$ Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":19180,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,310],"tags":[427,314,18],"series":[],"class_list":["post-9203","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-trigonometrica","tag-numeros-complexos"],"views":1248,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat71.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9203","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=9203"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9203\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19180"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9203"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9203"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9203"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=9203"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}