{"id":9180,"date":"2012-05-21T00:00:07","date_gmt":"2012-05-20T23:00:07","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=9180"},"modified":"2021-12-29T13:15:33","modified_gmt":"2021-12-29T13:15:33","slug":"represente-na-forma-trigonometrica","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=9180","title":{"rendered":"Represente na forma trigonom\u00e9trica"},"content":{"rendered":"<p><ul id='GTTabs_ul_9180' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_9180' class='GTTabs_curr'><a  id=\"9180_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_9180' ><a  id=\"9180_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_9180'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Represente na forma trigonom\u00e9trica:<\/p>\n<ol>\n<li>\u00a0$z =\u00a0 &#8211; 3\\operatorname{cis} \\theta $<\/li>\n<li>$z = 2\\cos \\theta\u00a0 &#8211; 2i\\operatorname{sen} \\theta $<\/li>\n<li>$z =\u00a0 &#8211; \\cos \\theta\u00a0 &#8211; i\\operatorname{sen} \\theta $<\/li>\n<li>$z = \\frac{1}{{2\\operatorname{cis} \\left( {\\frac{\\pi }{3} &#8211; \\theta } \\right)}}$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_9180' onClick='GTTabs_show(1,9180)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_9180'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{ &#8211; 3\\operatorname{cis} \\theta } \\\\<br \/>\n{}&amp; = &amp;{3\\operatorname{cis} \\left( {\\pi\u00a0 + \\theta } \\right)}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{2\\cos \\theta\u00a0 &#8211; 2i\\operatorname{sen} \\theta } \\\\<br \/>\n{}&amp; = &amp;{2\\cos \\left( { &#8211; \\theta } \\right) + 2i\\operatorname{sen} \\left( { &#8211; \\theta } \\right)} \\\\<br \/>\n{}&amp; = &amp;{2\\operatorname{cis} \\left( { &#8211; \\theta } \\right)}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{ &#8211; \\cos \\theta\u00a0 &#8211; i\\operatorname{sen} \\theta } \\\\<br \/>\n{}&amp; = &amp;{\\cos \\left( {\\pi\u00a0 + \\theta } \\right) + i\\operatorname{sen} \\left( {\\pi\u00a0 + \\theta } \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\operatorname{cis} \\left( {\\pi\u00a0 + \\theta } \\right)}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{\\frac{1}{{2\\operatorname{cis} \\left( {\\frac{\\pi }{3} &#8211; \\theta } \\right)}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{1}{2}\\operatorname{cis} \\left( { &#8211; \\frac{\\pi }{3} + \\theta } \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\frac{1}{2}\\operatorname{cis} \\left( {\\theta\u00a0 &#8211; \\frac{\\pi }{3}} \\right)}<br \/>\n\\end{array}$$<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_9180' onClick='GTTabs_show(0,9180)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Represente na forma trigonom\u00e9trica: \u00a0$z =\u00a0 &#8211; 3\\operatorname{cis} \\theta $ $z = 2\\cos \\theta\u00a0 &#8211; 2i\\operatorname{sen} \\theta $ $z =\u00a0 &#8211; \\cos \\theta\u00a0 &#8211; i\\operatorname{sen} \\theta $ $z = \\frac{1}{{2\\operatorname{cis} \\left(&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19181,"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-9180","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":1862,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat72.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9180","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=9180"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9180\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19181"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9180"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9180"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9180"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=9180"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}