{"id":8999,"date":"2012-05-10T01:52:24","date_gmt":"2012-05-10T00:52:24","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=8999"},"modified":"2022-01-14T02:17:46","modified_gmt":"2022-01-14T02:17:46","slug":"determine-os-outros-vertices-do-quadrado","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=8999","title":{"rendered":"Determine os outros v\u00e9rtices do quadrado"},"content":{"rendered":"<p><ul id='GTTabs_ul_8999' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_8999' class='GTTabs_curr'><a  id=\"8999_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_8999' ><a  id=\"8999_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_8999'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Sendo o afixo A de ${z_A} = 2 &#8211; 3i$ um dos v\u00e9rtices de um quadrado [OABC], determine os outros v\u00e9rtices, B e C, desse quadrado.<\/p>\n<p>(Pode obter mais do que uma solu\u00e7\u00e3o)<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_8999' onClick='GTTabs_show(1,8999)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_8999'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p style=\"text-align: center;\"><script src=\"https:\/\/cdn.geogebra.org\/apps\/deployggb.js\"><\/script>\r\n<div id=\"ggbApplet\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet\",\r\n\"width\":626,\r\n\"height\":437,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 59 || 1 501 67 , 5 19 , 72 | 2 15 45 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is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator, DA=Data Analysis, FI=Function Inspector, PV=Python, macro=Macro View\r\nvar views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 0,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0};\r\nvar applet = new GGBApplet(parameters, '5.0', views);\r\nwindow.onload = function() {applet.inject('ggbApplet')};\r\n<\/script><br \/>\n\u00ad<\/p>\n<p>H\u00e1 duas solu\u00e7\u00f5es:<\/p>\n<p style=\"text-align: center;\"><strong>Quadrado [OABC]<\/strong><\/p>\n<p>$$\\begin{array}{*{20}{l}}<br \/>\n{{z_C}}&amp; = &amp;{i{z_A}}&amp;{}&amp;{}&amp;{{z_B}}&amp; = &amp;{{z_A} + {z_C}} \\\\<br \/>\n{}&amp; = &amp;{i\\left( {2 &#8211; 3i} \\right)}&amp;{}&amp;{}&amp;{}&amp; = &amp;{\\left( {2 &#8211; 3i} \\right) + \\left( {3 + 2i} \\right)} \\\\<br \/>\n{}&amp; = &amp;{3 + 2i}&amp;{}&amp;{}&amp;{}&amp; = &amp;{5 &#8211; i}<br \/>\n\\end{array}$$<\/p>\n<p style=\"text-align: center;\">\u00a0<strong>Quadrado [OAB&#8217;C&#8217;]<\/strong><\/p>\n<p>$$\\begin{array}{*{20}{l}}<br \/>\n{{z_{C&#8217;}}}&amp; = &amp;{ &#8211; i{z_A}}&amp;{}&amp;{}&amp;{{z_{B&#8217;}}}&amp; = &amp;{{z_A} + {z_{C&#8217;}}} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; i\\left( {2 &#8211; 3i} \\right)}&amp;{}&amp;{}&amp;{}&amp; = &amp;{\\left( {2 &#8211; 3i} \\right) + \\left( { &#8211; 3 &#8211; 2i} \\right)} \\\\<br \/>\n{}&amp; = &amp;{ &#8211; 3 &#8211; 2i}&amp;{}&amp;{}&amp;{}&amp; = &amp;{ &#8211; 1 &#8211; 5i}<br \/>\n\\end{array}$$<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_8999' onClick='GTTabs_show(0,8999)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Sendo o afixo A de ${z_A} = 2 &#8211; 3i$ um dos v\u00e9rtices de um quadrado [OABC], determine os outros v\u00e9rtices, B e C, desse quadrado. 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