{"id":8943,"date":"2012-05-06T21:22:16","date_gmt":"2012-05-06T20:22:16","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=8943"},"modified":"2021-12-29T00:51:52","modified_gmt":"2021-12-29T00:51:52","slug":"escreva-na-forma-a-bi","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=8943","title":{"rendered":"Escreva na forma $a + bi$"},"content":{"rendered":"<p><ul id='GTTabs_ul_8943' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_8943' class='GTTabs_curr'><a  id=\"8943_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_8943' ><a  id=\"8943_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_8943'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Escreva na forma $a + bi$:<\/p>\n<ol>\n<li>$\\frac{5}{{3 &#8211; i}}$<\/li>\n<li>$\\frac{{2 + i}}{{2 &#8211; i}}$<\/li>\n<li>$\\frac{{3 + 2i}}{{5i}}$<\/li>\n<li>${i^{101}}$<\/li>\n<li>${i^{1999}} &#8211; 2$<\/li>\n<li>${i^{4n}} &#8211; 2{i^{4n + 3}}$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_8943' onClick='GTTabs_show(1,8943)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_8943'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{\\frac{5}{{3 &#8211; i}}}&amp; = &amp;{\\frac{5}{{3 &#8211; i}} \\times \\frac{{3 + i}}{{3 + i}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{15 + 5i}}{{{3^2} + 1}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{3}{2} + \\frac{1}{2}i}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{\\frac{{2 + i}}{{2 &#8211; i}}}&amp; = &amp;{\\frac{{2 + i}}{{2 &#8211; i}} \\times \\frac{{2 + i}}{{2 + i}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{4 + 2i + 2i &#8211; 1}}{{4 + 1}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{3}{5} + \\frac{4}{5}i}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{\\frac{{3 + 2i}}{{5i}}}&amp; = &amp;{\\frac{{3 + 2i}}{{5i}} \\times \\frac{{ &#8211; i}}{{ &#8211; i}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{2 &#8211; 3i}}{5}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{2}{5} &#8211; \\frac{3}{5}i}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{{i^{101}}}&amp; = &amp;{{{\\left( {{i^4}} \\right)}^{25}} \\times i} \\\\<br \/>\n{}&amp; = &amp;{{1^{25}} \\times i} \\\\<br \/>\n{}&amp; = &amp;i<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{{i^{1999}} &#8211; 2}&amp; = &amp;{{{\\left( {{i^4}} \\right)}^{499}} \\times {i^3} &#8211; 2} \\\\<br \/>\n{}&amp; = &amp;{1 \\times \\left( { &#8211; i} \\right) &#8211; 2} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; 2 &#8211; i}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{{i^{4n}} &#8211; 2{i^{4n + 3}}}&amp; = &amp;{{{\\left( {{i^4}} \\right)}^n} &#8211; 2 \\times {{\\left( {{i^4}} \\right)}^n} \\times {i^3}} \\\\<br \/>\n{}&amp; = &amp;{1 &#8211; 2 \\times 1 \\times \\left( { &#8211; i} \\right)} \\\\<br \/>\n{}&amp; = &amp;{1 + 2i}<br \/>\n\\end{array}$$<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_8943' onClick='GTTabs_show(0,8943)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Escreva na forma $a + bi$: $\\frac{5}{{3 &#8211; i}}$ $\\frac{{2 + i}}{{2 &#8211; i}}$ $\\frac{{3 + 2i}}{{5i}}$ ${i^{101}}$ ${i^{1999}} &#8211; 2$ ${i^{4n}} &#8211; 2{i^{4n + 3}}$ Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":19539,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,310],"tags":[427,18],"series":[],"class_list":["post-8943","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-numeros-complexos"],"views":1245,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat158.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8943","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=8943"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8943\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8943"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8943"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8943"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=8943"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}