{"id":8955,"date":"2012-05-06T22:26:59","date_gmt":"2012-05-06T21:26:59","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=8955"},"modified":"2021-12-29T00:59:14","modified_gmt":"2021-12-29T00:59:14","slug":"escreva-na-forma-a-bi-os-numeros-complexos-seguintes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=8955","title":{"rendered":"Escreva na forma $a + bi$ os n\u00fameros complexos seguintes"},"content":{"rendered":"<p><ul id='GTTabs_ul_8955' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_8955' class='GTTabs_curr'><a  id=\"8955_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_8955' ><a  id=\"8955_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_8955'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Considere os n\u00fameros complexos $$\\begin{array}{*{20}{c}}<br \/>\n{z = 1 &#8211; 2i}&amp;{}&amp;{\\text{e}}&amp;{}&amp;{w =\u00a0 &#8211; 5 + 3i}<br \/>\n\\end{array}$$ e escreva na forma $a + bi$ os n\u00fameros complexos seguintes:<\/p>\n<ol>\n<li>$z + w$<\/li>\n<li>$4z &#8211; 5w$<\/li>\n<li>$z.w$<\/li>\n<li>$\\frac{z}{w}$<\/li>\n<li>${z^2} &#8211; \\frac{1}{z}$<\/li>\n<li>$\\frac{2}{{{z^3}}}$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_8955' onClick='GTTabs_show(1,8955)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_8955'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{z + w}&amp; = &amp;{\\left( {1 &#8211; 2i} \\right) + \\left( { &#8211; 5 + 3i} \\right)} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; 4 + i}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{4z &#8211; 5w}&amp; = &amp;{4\\left( {1 &#8211; 2i} \\right) &#8211; 5\\left( { &#8211; 5 + 3i} \\right)} \\\\<br \/>\n{}&amp; = &amp;{4 &#8211; 8i + 25 &#8211; 15i} \\\\<br \/>\n{}&amp; = &amp;{29 &#8211; 23i}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{z.w}&amp; = &amp;{\\left( {1 &#8211; 2i} \\right).\\left( { &#8211; 5 + 3i} \\right)} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; 5 + 3i + 10i + 6} \\\\<br \/>\n{}&amp; = &amp;{1 + 13i}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{\\frac{z}{w}}&amp; = &amp;{\\frac{{1 &#8211; 2i}}{{ &#8211; 5 + 3i}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{1 &#8211; 2i}}{{ &#8211; 5 + 3i}} \\times \\frac{{ &#8211; 5 &#8211; 3i}}{{ &#8211; 5 &#8211; 3i}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{ &#8211; 5 &#8211; 3i + 10i &#8211; 6}}{{25 + 9}}} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; \\frac{{11}}{{34}} + \\frac{7}{{34}}i}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{{z^2} &#8211; \\frac{1}{z}}&amp; = &amp;{{{\\left( {1 &#8211; 2i} \\right)}^2} &#8211; \\frac{1}{{1 &#8211; 2i}}} \\\\<br \/>\n{}&amp; = &amp;{1 &#8211; 4i &#8211; 4 &#8211; \\frac{1}{{1 &#8211; 2i}} \\times \\frac{{1 + 2i}}{{1 + 2i}}} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; 3 &#8211; 4i &#8211; \\frac{{1 + 2i}}{{1 + 4}}} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; 3 &#8211; 4i &#8211; \\frac{1}{5} &#8211; \\frac{2}{5}i} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; \\frac{{16}}{5} &#8211; \\frac{{22}}{5}i}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{\\frac{2}{{{z^3}}}}&amp; = &amp;{\\frac{2}{{{{\\left( {1 &#8211; 2i} \\right)}^3}}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{2}{{\\left( {1 &#8211; 4i &#8211; 4} \\right)\\left( {1 &#8211; 2i} \\right)}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{2}{{ &#8211; 3 + 6i &#8211; 4i &#8211; 8}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{2}{{ &#8211; 11 + 2i}} \\times \\frac{{ &#8211; 11 &#8211; 2i}}{{ &#8211; 11 &#8211; 2i}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{ &#8211; 22 &#8211; 4i}}{{121 + 4}}} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; \\frac{{22}}{{125}} &#8211; \\frac{4}{{125}}i}<br \/>\n\\end{array}$$<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_8955' onClick='GTTabs_show(0,8955)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considere os n\u00fameros complexos $$\\begin{array}{*{20}{c}} {z = 1 &#8211; 2i}&amp;{}&amp;{\\text{e}}&amp;{}&amp;{w =\u00a0 &#8211; 5 + 3i} \\end{array}$$ e escreva na forma $a + bi$ os n\u00fameros complexos seguintes: $z + w$ $4z&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14057,"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-8955","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":1976,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat02.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8955","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=8955"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8955\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14057"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8955"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8955"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8955"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=8955"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}