{"id":9043,"date":"2012-05-14T22:20:47","date_gmt":"2012-05-14T21:20:47","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=9043"},"modified":"2022-01-14T02:26:28","modified_gmt":"2022-01-14T02:26:28","slug":"considere-o-numero-complexo-z-alpha-alpha-2i","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=9043","title":{"rendered":"Considere o n\u00famero complexo $z = \\alpha  + {\\alpha ^2}i$"},"content":{"rendered":"<p><ul id='GTTabs_ul_9043' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_9043' class='GTTabs_curr'><a  id=\"9043_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_9043' ><a  id=\"9043_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_9043'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Considere o n\u00famero complexo $z = \\alpha\u00a0 + {\\alpha ^2}i$.<\/p>\n<p>Represente no plano complexo as imagens de $z$ para $\\alpha\u00a0 = 1$ e depois para $\\alpha\u00a0 =\u00a0 &#8211; 2$, $\\alpha\u00a0 = 0$ e $\\alpha\u00a0 = 3$.<\/p>\n<p>Qual \u00e9 o conjunto dos pontos imagem de $z$ quando $\\alpha $ percorre $\\mathbb{R}$?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_9043' onClick='GTTabs_show(1,9043)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_9043'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Para os valores de\u00a0$\\alpha $ dados, obt\u00e9m-se: $$\\begin{array}{*{20}{l}}<br \/>\n{\\alpha\u00a0 = 1}&amp;:&amp;{{z_A} = 1 + i} \\\\<br \/>\n{\\alpha\u00a0 =\u00a0 &#8211; 2}&amp;:&amp;{{z_B} =\u00a0 &#8211; 2 + 4i} \\\\<br \/>\n{\\alpha\u00a0 = 0}&amp;:&amp;{{z_C} = 0 + 0i} \\\\<br \/>\n{\\alpha\u00a0 = 3}&amp;:&amp;{{z_D} = 3 + 9i}<br \/>\n\\end{array}$$<\/p>\n<\/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\":511,\r\n\"height\":430,\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 , 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Represente no plano complexo as imagens de $z$ para $\\alpha\u00a0 = 1$ e depois para $\\alpha\u00a0 =\u00a0 &#8211; 2$, $\\alpha\u00a0 =&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14080,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,310],"tags":[427,18,313],"series":[],"class_list":["post-9043","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","tag-plano-de-argand"],"views":1728,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat25.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9043","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=9043"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9043\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14080"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9043"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9043"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9043"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=9043"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}