{"id":9271,"date":"2012-05-22T00:41:00","date_gmt":"2012-05-21T23:41:00","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=9271"},"modified":"2021-12-29T15:26:29","modified_gmt":"2021-12-29T15:26:29","slug":"represente-na-forma-trigonometrica-3","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=9271","title":{"rendered":"Represente na forma trigonom\u00e9trica"},"content":{"rendered":"<p><ul id='GTTabs_ul_9271' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_9271' class='GTTabs_curr'><a  id=\"9271_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_9271' ><a  id=\"9271_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_9271'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Represente, na forma trigonom\u00e9trica, o n\u00famero $$\\frac{{1 + \\sqrt 2\u00a0 + i}}{{1 + \\sqrt 2\u00a0 &#8211; i}}$$<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_9271' onClick='GTTabs_show(1,9271)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_9271'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>$$\\begin{array}{*{20}{l}}<br \/>\n{\\frac{{1 + \\sqrt 2\u00a0 + i}}{{1 + \\sqrt 2\u00a0 &#8211; i}}}&amp; = &amp;{\\frac{{1 + \\sqrt 2\u00a0 + i}}{{1 + \\sqrt 2\u00a0 &#8211; i}} \\times \\frac{{1 + \\sqrt 2\u00a0 + i}}{{1 + \\sqrt 2\u00a0 + i}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{{{\\left( {1 + \\sqrt 2\u00a0 + i} \\right)}^2}}}{{{{\\left( {1 + \\sqrt 2 } \\right)}^2} + 1}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{{{\\left( {1 + \\sqrt 2 } \\right)}^2} + 2\\left( {1 + \\sqrt 2 } \\right)i &#8211; 1}}{{1 + 2\\sqrt 2\u00a0 + 2 + 1}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{1 + 2\\sqrt 2\u00a0 + 2 + 2\\left( {1 + \\sqrt 2 } \\right)i &#8211; 1}}{{4 + 2\\sqrt 2 }}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{2\\left( {1 + \\sqrt 2 } \\right) + 2\\left( {1 + \\sqrt 2 } \\right)i}}{{2\\left( {2 + \\sqrt 2 } \\right)}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{\\left( {1 + \\sqrt 2 } \\right) + \\left( {1 + \\sqrt 2 } \\right)i}}{{\\left( {2 + \\sqrt 2 } \\right)}} \\times \\frac{{2 &#8211; \\sqrt 2 }}{{2 &#8211; \\sqrt 2 }}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{\\left( {2 &#8211; \\sqrt 2\u00a0 + 2\\sqrt 2\u00a0 &#8211; 2} \\right) + \\left( {2 &#8211; \\sqrt 2\u00a0 + 2\\sqrt 2\u00a0 &#8211; 2} \\right)i}}{{4 &#8211; 2}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{\\sqrt 2 }}{2} + \\frac{{\\sqrt 2 }}{2}i} \\\\<br \/>\n{}&amp; = &amp;{\\operatorname{cis} \\frac{\\pi }{4}}<br \/>\n\\end{array}$$<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_9271' onClick='GTTabs_show(0,9271)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Represente, na forma trigonom\u00e9trica, o n\u00famero $$\\frac{{1 + \\sqrt 2\u00a0 + i}}{{1 + \\sqrt 2\u00a0 &#8211; i}}$$ Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":19189,"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-9271","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":3536,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat75.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9271","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=9271"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9271\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19189"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9271"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9271"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9271"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=9271"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}