{"id":9234,"date":"2012-05-21T20:17:28","date_gmt":"2012-05-21T19:17:28","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=9234"},"modified":"2021-12-29T14:49:05","modified_gmt":"2021-12-29T14:49:05","slug":"calcule-4","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=9234","title":{"rendered":"Calcule"},"content":{"rendered":"<p><ul id='GTTabs_ul_9234' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_9234' class='GTTabs_curr'><a  id=\"9234_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_9234' ><a  id=\"9234_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_9234'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Sendo $$\\begin{array}{*{20}{c}}<br \/>\n{{z_1} = 16\\operatorname{cis} \\frac{\\pi }{4}}&amp;{\\text{e}}&amp;{{z_2} = 16\\operatorname{cis} \\frac{{3\\pi }}{4}}<br \/>\n\\end{array}$$ calcule:<\/p>\n<ol>\n<li>${z_1} + {z_2}$<\/li>\n<li>${z_1} &#8211; {z_2}$<\/li>\n<li>${\\left( {\\frac{{{z_1} + {z_2}}}{{{z_1} &#8211; {z_2}}}} \\right)^3}$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_9234' onClick='GTTabs_show(1,9234)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_9234'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{{z_1} + {z_2}}&amp; = &amp;{16\\operatorname{cis} \\frac{\\pi }{4} + 16\\operatorname{cis} \\frac{{3\\pi }}{4}} \\\\<br \/>\n{}&amp; = &amp;{16\\left( {\\frac{{\\sqrt 2 }}{2} + \\frac{{\\sqrt 2 }}{2}i} \\right) + 16\\left( { &#8211; \\frac{{\\sqrt 2 }}{2} + \\frac{{\\sqrt 2 }}{2}i} \\right)} \\\\<br \/>\n{}&amp; = &amp;{16\\sqrt 2 i}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{{z_1} &#8211; {z_2}}&amp; = &amp;{16\\operatorname{cis} \\frac{\\pi }{4} &#8211; 16\\operatorname{cis} \\frac{{3\\pi }}{4}} \\\\<br \/>\n{}&amp; = &amp;{16\\left( {\\frac{{\\sqrt 2 }}{2} + \\frac{{\\sqrt 2 }}{2}i} \\right) &#8211; 16\\left( { &#8211; \\frac{{\\sqrt 2 }}{2} + \\frac{{\\sqrt 2 }}{2}i} \\right)} \\\\<br \/>\n{}&amp; = &amp;{16\\sqrt 2 }<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{{{\\left( {\\frac{{{z_1} + {z_2}}}{{{z_1} &#8211; {z_2}}}} \\right)}^3}}&amp; = &amp;{{{\\left( {\\frac{{16\\sqrt 2 i}}{{16\\sqrt 2 }}} \\right)}^3}} \\\\<br \/>\n{}&amp; = &amp;{{i^3}} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; i}<br \/>\n\\end{array}$$<\/li>\n<\/ol>\n<blockquote>\n<p><strong>Nota<\/strong>: N\u00c3O existem regras operat\u00f3rias relativas \u00e0 adi\u00e7\u00e3o e subtra\u00e7\u00e3o de n\u00fameros complexos na forma trigonom\u00e9trica!<\/p>\n<\/blockquote>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_9234' onClick='GTTabs_show(0,9234)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Sendo $$\\begin{array}{*{20}{c}} {{z_1} = 16\\operatorname{cis} \\frac{\\pi }{4}}&amp;{\\text{e}}&amp;{{z_2} = 16\\operatorname{cis} \\frac{{3\\pi }}{4}} \\end{array}$$ calcule: ${z_1} + {z_2}$ ${z_1} &#8211; {z_2}$ ${\\left( {\\frac{{{z_1} + {z_2}}}{{{z_1} &#8211; {z_2}}}} \\right)^3}$ Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":19172,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,310],"tags":[427,315,314,18],"series":[],"class_list":["post-9234","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-forma-trigonometrica","tag-numeros-complexos"],"views":1834,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat63.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9234","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=9234"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9234\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9234"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9234"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9234"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=9234"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}