{"id":9282,"date":"2012-05-22T02:14:43","date_gmt":"2012-05-22T01:14:43","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=9282"},"modified":"2021-12-29T15:31:27","modified_gmt":"2021-12-29T15:31:27","slug":"calcule-o-valor-de","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=9282","title":{"rendered":"Calcule o valor de"},"content":{"rendered":"<p><ul id='GTTabs_ul_9282' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_9282' class='GTTabs_curr'><a  id=\"9282_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_9282' ><a  id=\"9282_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_9282'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Calcule o valor de: $${{{\\left( {\\frac{{\\cos \\theta\u00a0 &#8211; i\\operatorname{sen} \\theta }}{{\\operatorname{sen} \\theta\u00a0 + i\\cos \\theta }}} \\right)}^5}}$$<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_9282' onClick='GTTabs_show(1,9282)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_9282'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Ora,<\/p>\n<p>$$\\begin{array}{*{20}{l}}<br \/>\n{{{\\left( {\\frac{{\\cos \\theta\u00a0 &#8211; i\\operatorname{sen} \\theta }}{{\\operatorname{sen} \\theta\u00a0 + i\\cos \\theta }}} \\right)}^5}}&amp; = &amp;{{{\\left( {\\frac{{\\operatorname{cis} \\left( { &#8211; \\theta } \\right)}}{{\\cos \\left( {\\frac{\\pi }{2} &#8211; \\theta } \\right) + i\\operatorname{sen} \\left( {\\frac{\\pi }{2} &#8211; \\theta } \\right)}}} \\right)}^5}} \\\\<br \/>\n{}&amp; = &amp;{{{\\left( {\\frac{{\\operatorname{cis} \\left( { &#8211; \\theta } \\right)}}{{\\operatorname{cis} \\left( {\\frac{\\pi }{2} &#8211; \\theta } \\right)}}} \\right)}^5}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{\\operatorname{cis} \\left( { &#8211; 5\\theta } \\right)}}{{\\operatorname{cis} \\left( {\\frac{{5\\pi }}{2} &#8211; 5\\theta } \\right)}}} \\\\<br \/>\n{}&amp; = &amp;{\\operatorname{cis} \\left( { &#8211; 5\\theta\u00a0 &#8211; \\frac{{5\\pi }}{2} + 5\\theta } \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\operatorname{cis} \\left( { &#8211; \\frac{{5\\pi }}{2}} \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\operatorname{cis} \\left( { &#8211; \\frac{\\pi }{2}} \\right)} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; i}<br \/>\n\\end{array}$$<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_9282' onClick='GTTabs_show(0,9282)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Calcule o valor de: $${{{\\left( {\\frac{{\\cos \\theta\u00a0 &#8211; i\\operatorname{sen} \\theta }}{{\\operatorname{sen} \\theta\u00a0 + i\\cos \\theta }}} \\right)}^5}}$$ Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/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":[427,314,18],"series":[],"class_list":["post-9282","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":1962,"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\/9282","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=9282"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9282\/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=9282"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9282"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9282"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=9282"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}