{"id":9030,"date":"2012-05-14T00:42:43","date_gmt":"2012-05-13T23:42:43","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=9030"},"modified":"2022-01-27T00:17:32","modified_gmt":"2022-01-27T00:17:32","slug":"resolva-a-equacao","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=9030","title":{"rendered":"Resolva a equa\u00e7\u00e3o"},"content":{"rendered":"<p><ul id='GTTabs_ul_9030' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_9030' class='GTTabs_curr'><a  id=\"9030_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_9030' ><a  id=\"9030_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_9030'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<ol>\n<li>Em $C$, fatorize ${z^4} &#8211; 16$ num produto de quatro fatores.<\/li>\n<li>Resolva a equa\u00e7\u00e3o ${z^4} &#8211; 16 = 0$.<\/li>\n<li>Marque no plano complexo as imagens A, B, C e D das solu\u00e7\u00f5es e verifique que s\u00e3o v\u00e9rtices de um quadrado.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_9030' onClick='GTTabs_show(1,9030)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_9030'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{{z^4} &#8211; 16}&amp; = &amp;{{{\\left( {{z^2}} \\right)}^2} &#8211; {4^2}} \\\\<br \/>\n{}&amp; = &amp;{\\left( {{z^2} + 4} \\right)\\left( {{z^2} &#8211; 4} \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\left( {{z^2} + 4} \\right)\\left( {z + 2} \\right)\\left( {z &#8211; 2} \\right)}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{{z^4} &#8211; 16 = 0}&amp; \\Leftrightarrow &amp;{\\left( {{z^2} + 4} \\right)\\left( {z + 2} \\right)\\left( {z &#8211; 2} \\right) = 0} \\\\<br \/>\n{}&amp; = &amp;{\\begin{array}{*{20}{l}}<br \/>\n{z =\u00a0 &#8211; 2i}&amp; \\vee &amp;{z = 2i}&amp; \\vee &amp;{z =\u00a0 &#8211; 2}&amp; \\vee &amp;{z = 2}<br \/>\n\\end{array}}<br \/>\n\\end{array}$$<br \/>\n\u00ad<\/li>\n<li>\n<p><div id=\"attachment_9033\" style=\"width: 415px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/05\/12pag139-38.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-9033\" data-attachment-id=\"9033\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=9033\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/05\/12pag139-38.png\" data-orig-size=\"405,309\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Quadrado\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/05\/12pag139-38.png\" class=\"size-full wp-image-9033\" title=\"Quadrado\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/05\/12pag139-38.png\" alt=\"\" width=\"405\" height=\"309\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/05\/12pag139-38.png 405w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/05\/12pag139-38-300x228.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/05\/12pag139-38-150x114.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/05\/12pag139-38-400x305.png 400w\" sizes=\"auto, (max-width: 405px) 100vw, 405px\" \/><\/a><p id=\"caption-attachment-9033\" class=\"wp-caption-text\">Os afixos das solu\u00e7\u00f5es da equa\u00e7\u00e3o s\u00e3o v\u00e9rtices de um quadrado<\/p><\/div><\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_9030' onClick='GTTabs_show(0,9030)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Em $C$, fatorize ${z^4} &#8211; 16$ num produto de quatro fatores. Resolva a equa\u00e7\u00e3o ${z^4} &#8211; 16 = 0$. Marque no plano complexo as imagens A, B, C e D das&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":21077,"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-9030","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":1353,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/05\/12V3Pag139-38_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9030","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=9030"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9030\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21077"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9030"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9030"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9030"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=9030"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}