{"id":8972,"date":"2012-05-09T22:45:26","date_gmt":"2012-05-09T21:45:26","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=8972"},"modified":"2022-01-14T02:14:04","modified_gmt":"2022-01-14T02:14:04","slug":"representacao-geometrica-dos-numeros-complexos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=8972","title":{"rendered":"Representa\u00e7\u00e3o geom\u00e9trica dos n\u00fameros complexos"},"content":{"rendered":"<p>Explora\u00e7\u00e3o da representa\u00e7\u00e3o geom\u00e9trica de opera\u00e7\u00f5es com n\u00fameros complexos:<\/p>\n<ul>\n<li data-tadv-p=\"keep\">Conjugado e sim\u00e9trico de um n\u00famero complexo<\/li>\n<li data-tadv-p=\"keep\">Adi\u00e7\u00e3o de dois n\u00fameros complexos<\/li>\n<li data-tadv-p=\"keep\">Multiplica\u00e7\u00e3o de um n\u00famero complexo pela unidade imagin\u00e1ria<\/li>\n<li data-tadv-p=\"keep\">Multiplica\u00e7\u00e3o de dois n\u00fameros complexos<\/li>\n<\/ul>\n<p><ul id='GTTabs_ul_8972' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_8972' class='GTTabs_curr'><a  id=\"8972_0\" onMouseOver=\"GTTabsShowLinks('Conjugado e sim\u00e9trico'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Conjugado e sim\u00e9trico<\/a><\/li>\n<li id='GTTabs_li_1_8972' ><a  id=\"8972_1\" onMouseOver=\"GTTabsShowLinks('Soma ${z_1} + {z_2}$'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Soma ${z_1} + {z_2}$<\/a><\/li>\n<li id='GTTabs_li_2_8972' ><a  id=\"8972_2\" onMouseOver=\"GTTabsShowLinks('Produto $iz$'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Produto $iz$<\/a><\/li>\n<li id='GTTabs_li_3_8972' ><a  id=\"8972_3\" onMouseOver=\"GTTabsShowLinks('Produto ${z_1}.{z_2}$'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Produto ${z_1}.{z_2}$<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_8972'>\n<span class='GTTabs_titles'><b>Conjugado e 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instead of ggbBase64 to load a material from GeoGebraTube\r\n\/\/ 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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><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_8972' onClick='GTTabs_show(1,8972)'>Soma ${z_1} + {z_2}$ &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_8972'>\n<span class='GTTabs_titles'><b>Soma ${z_1} + {z_2}$<\/b><\/span><\/p>\n<p style=\"text-align: center;\"><body>\r\n<div id=\"ggbApplet2\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet2\",\r\n\"width\":901,\r\n\"height\":524,\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 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 || 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 || 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 , 14 66 68 | 25 52 60 61 || 40 41 42 , 27 28 35 , 6\",\r\n\"showToolBarHelp\":false,\r\n\"showResetIcon\":true,\r\n\"enableLabelDrags\":false,\r\n\"enableShiftDragZoom\":false,\r\n\"enableRightClick\":false,\r\n\"errorDialogsActive\":false,\r\n\"useBrowserForJS\":false,\r\n\"preventFocus\":false,\r\n\"showFullscreenButton\":true,\r\n\"language\":\"pt\",\r\n\/\/ use this instead of ggbBase64 to load a material from GeoGebraTube\r\n\/\/ \"material_id\":12345,\r\n\"ggbBase64\":\"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\"};\r\n\/\/ 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 applet2 = new GGBApplet(parameters, '5.0', views);\r\nwindow.onload = function() {applet.inject('ggbApplet'); applet2.inject('ggbApplet2')};\r\n<\/script><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_8972' onClick='GTTabs_show(0,8972)'>&lt;&lt; Conjugado e sim\u00e9trico<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_8972' onClick='GTTabs_show(2,8972)'>Produto $iz$ &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_2_8972'>\n<span class='GTTabs_titles'><b>Produto $iz$<\/b><\/span><\/p>\n<p style=\"text-align: center;\"><div id=\"ggbApplet3\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet3\",\r\n\"width\":898,\r\n\"height\":523,\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 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 || 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 || 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 , 14 66 68 | 25 52 60 61 || 40 41 42 , 27 28 35 , 6\",\r\n\"showToolBarHelp\":false,\r\n\"showResetIcon\":true,\r\n\"enableLabelDrags\":false,\r\n\"enableShiftDragZoom\":false,\r\n\"enableRightClick\":false,\r\n\"errorDialogsActive\":false,\r\n\"useBrowserForJS\":false,\r\n\"preventFocus\":false,\r\n\"showFullscreenButton\":true,\r\n\"language\":\"pt\",\r\n\/\/ use this instead of ggbBase64 to load a material from GeoGebraTube\r\n\/\/ \"material_id\":12345,\r\n\"ggbBase64\":\"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\"};\r\n\/\/ 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 applet3 = new GGBApplet(parameters, '5.0', views);\r\nwindow.onload = function() {applet.inject('ggbApplet'); applet2.inject('ggbApplet2'); applet3.inject('ggbApplet3')};\r\n<\/script><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_8972' onClick='GTTabs_show(1,8972)'>&lt;&lt; Soma ${z_1} + {z_2}$<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_8972' onClick='GTTabs_show(3,8972)'>Produto ${z_1}.{z_2}$ &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_3_8972'>\n<span class='GTTabs_titles'><b>Produto ${z_1}.{z_2}$<\/b><\/span><\/p>\n<p style=\"text-align: center;\"><div id=\"ggbApplet4\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet4\",\r\n\"width\":902,\r\n\"height\":523,\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 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 || 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 || 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 , 14 66 68 | 25 52 60 61 || 40 41 42 , 27 28 35 , 6\",\r\n\"showToolBarHelp\":false,\r\n\"showResetIcon\":true,\r\n\"enableLabelDrags\":false,\r\n\"enableShiftDragZoom\":false,\r\n\"enableRightClick\":false,\r\n\"errorDialogsActive\":false,\r\n\"useBrowserForJS\":false,\r\n\"preventFocus\":false,\r\n\"showFullscreenButton\":true,\r\n\"language\":\"pt\",\r\n\/\/ use this instead of ggbBase64 to load a material from GeoGebraTube\r\n\/\/ 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n\u00fameros complexos Multiplica\u00e7\u00e3o de um n\u00famero complexo pela unidade imagin\u00e1ria Multiplica\u00e7\u00e3o de dois n\u00fameros complexos&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19234,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,310],"tags":[427,312,18],"series":[],"class_list":["post-8972","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-conjugado","tag-numeros-complexos"],"views":2162,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat76.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8972","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=8972"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/8972\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19234"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8972"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8972"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8972"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=8972"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}