{"id":9186,"date":"2012-05-21T00:22:41","date_gmt":"2012-05-20T23:22:41","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=9186"},"modified":"2021-12-29T13:18:31","modified_gmt":"2021-12-29T13:18:31","slug":"calcule-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=9186","title":{"rendered":"Calcule"},"content":{"rendered":"<p><ul id='GTTabs_ul_9186' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_9186' class='GTTabs_curr'><a  id=\"9186_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_9186' ><a  id=\"9186_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_9186'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Calcule:<\/p>\n<ol>\n<li>$$\\frac{{2\\operatorname{cis} \\frac{\\pi }{3}}}{{4\\operatorname{cis} \\left( {\\frac{{2\\pi }}{3}} \\right)}}$$<\/li>\n<li>$$\\frac{{ &#8211; 2}}{{\\operatorname{cis} \\left( { &#8211; \\theta } \\right)}}$$<\/li>\n<li>$$\\frac{{ &#8211; \\operatorname{cis} \\frac{\\pi }{6}}}{{2\\operatorname{cis} \\theta }}$$<\/li>\n<li>$$\\left( {2\\operatorname{cis} \\frac{{5\\pi }}{6}} \\right) \\times \\left[ {3\\operatorname{cis} \\left( { &#8211; \\frac{{2\\pi }}{3}} \\right)} \\right]$$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_9186' onClick='GTTabs_show(1,9186)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_9186'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p><strong>Forma trigonom\u00e9trica do quociente<\/strong>:<\/p>\n<p style=\"text-align: center;\">Se ${z_1} = {\\rho _1}\\operatorname{cis} \\left( {{\\theta _1}} \\right)$ e ${z_2} = {\\rho _2}\\operatorname{cis} \\left( {{\\theta _2}} \\right)$ s\u00e3o dois n\u00fameros complexos n\u00e3o nulos, ent\u00e3o $$\\frac{{{z_1}}}{{{z_2}}} = \\frac{{{\\rho _1}}}{{{\\rho _2}}}\\operatorname{cis} \\left( {{\\theta _1} &#8211; {\\theta _2}} \\right)$$<\/p>\n<\/blockquote>\n<ol>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{\\frac{{2\\operatorname{cis} \\frac{\\pi }{3}}}{{4\\operatorname{cis} \\left( {\\frac{{2\\pi }}{3}} \\right)}}}&amp; = &amp;{\\frac{2}{4}\\operatorname{cis} \\left( {\\frac{\\pi }{3} &#8211; \\frac{{2\\pi }}{3}} \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\frac{1}{2}\\operatorname{cis} \\left( { &#8211; \\frac{\\pi }{3}} \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\frac{1}{2}\\operatorname{cis} \\frac{{5\\pi }}{3}}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{\\frac{{ &#8211; 2}}{{\\operatorname{cis} \\left( { &#8211; \\theta } \\right)}}}&amp; = &amp;{\\frac{{2\\operatorname{cis} \\pi }}{{\\operatorname{cis} \\left( { &#8211; \\theta } \\right)}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{2}{1}\\operatorname{cis} \\left( {\\pi\u00a0 + \\theta } \\right)} \\\\<br \/>\n{}&amp; = &amp;{2\\operatorname{cis} \\left( {\\pi\u00a0 + \\theta } \\right)}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{\\frac{{ &#8211; \\operatorname{cis} \\frac{\\pi }{6}}}{{2\\operatorname{cis} \\theta }}}&amp; = &amp;{\\frac{{\\operatorname{cis} \\left( {\\pi\u00a0 + \\frac{\\pi }{6}} \\right)}}{{2\\operatorname{cis} \\theta }}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{1}{2}\\operatorname{cis} \\left( {\\pi\u00a0 + \\frac{\\pi }{6} &#8211; \\theta } \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\frac{1}{2}\\operatorname{cis} \\left( {\\frac{{7\\pi }}{6} &#8211; \\theta } \\right)}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{\\left( {2\\operatorname{cis} \\frac{{5\\pi }}{6}} \\right) \\times \\left[ {3\\operatorname{cis} \\left( { &#8211; \\frac{{2\\pi }}{3}} \\right)} \\right]}&amp; = &amp;{\\left( {2 \\times 3} \\right)\\operatorname{cis} \\left( {\\frac{{5\\pi }}{6} + \\left( { &#8211; \\frac{{2\\pi }}{3}} \\right)} \\right)} \\\\<br \/>\n{}&amp; = &amp;{6\\operatorname{cis} \\frac{\\pi }{6}}<br \/>\n\\end{array}$$<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_9186' onClick='GTTabs_show(0,9186)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Calcule: $$\\frac{{2\\operatorname{cis} \\frac{\\pi }{3}}}{{4\\operatorname{cis} \\left( {\\frac{{2\\pi }}{3}} \\right)}}$$ $$\\frac{{ &#8211; 2}}{{\\operatorname{cis} \\left( { &#8211; \\theta } \\right)}}$$ $$\\frac{{ &#8211; \\operatorname{cis} \\frac{\\pi }{6}}}{{2\\operatorname{cis} \\theta }}$$ $$\\left( {2\\operatorname{cis} \\frac{{5\\pi }}{6}} \\right) \\times \\left[&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19601,"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-9186","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":1464,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat198.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9186","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=9186"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9186\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19601"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9186"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9186"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9186"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=9186"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}