{"id":9303,"date":"2012-05-22T17:59:11","date_gmt":"2012-05-22T16:59:11","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=9303"},"modified":"2021-12-29T22:44:42","modified_gmt":"2021-12-29T22:44:42","slug":"determine-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=9303","title":{"rendered":"Determine"},"content":{"rendered":"<p><ul id='GTTabs_ul_9303' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_9303' class='GTTabs_curr'><a  id=\"9303_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_9303' ><a  id=\"9303_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_9303'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Determine:<\/p>\n<ol>\n<li>as cinco ra\u00edzes quintas de\u00a0$z = 1$;<\/li>\n<li>as quatro ra\u00edzes quartas de $z = i$.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_9303' onClick='GTTabs_show(1,9303)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_9303'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>\u00a0As cinco ra\u00edzes quintas de $z = 1 = \\operatorname{cis} \\left( 0 \\right)$ s\u00e3o:<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{k = 0:}&amp;{{w_0} = \\sqrt[5]{1}\\operatorname{cis} \\left( {\\frac{0}{5}} \\right) = \\operatorname{cis} \\left( 0 \\right)} \\\\<br \/>\n{k = 1:}&amp;{{w_1} = \\sqrt[5]{1}\\operatorname{cis} \\left( {\\frac{0}{5} + \\frac{{2\\pi }}{5}} \\right) = \\operatorname{cis} \\left( {\\frac{{2\\pi }}{5}} \\right)} \\\\<br \/>\n{k = 2:}&amp;{{w_2} = \\sqrt[5]{1}\\operatorname{cis} \\left( {\\frac{0}{5} + \\frac{{4\\pi }}{5}} \\right) = \\operatorname{cis} \\left( {\\frac{{4\\pi }}{5}} \\right)} \\\\<br \/>\n{k = 3:}&amp;{{w_3} = \\sqrt[5]{1}\\operatorname{cis} \\left( {\\frac{0}{5} + \\frac{{6\\pi }}{5}} \\right) = \\operatorname{cis} \\left( {\\frac{{6\\pi }}{5}} \\right)} \\\\<br \/>\n{k = 4}&amp;{{w_4} = \\sqrt[5]{1}\\operatorname{cis} \\left( {\\frac{0}{5} + \\frac{{8\\pi }}{5}} \\right) = \\operatorname{cis} \\left( {\\frac{{8\\pi }}{5}} \\right)}<br \/>\n\\end{array}$$<br \/>\n\u00ad<\/li>\n<li>As quatros ra\u00edzes quartas de $z = i = \\operatorname{cis} \\left( {\\frac{\\pi }{2}} \\right)$ s\u00e3o:<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\n{k = 0:}&amp;{{w_0} = \\sqrt[4]{1}\\operatorname{cis} \\left( {\\frac{{\\tfrac{\\pi }{2}}}{4}} \\right) = \\operatorname{cis} \\left( {\\frac{\\pi }{8}} \\right)} \\\\<br \/>\n{k = 1:}&amp;{{w_1} = \\sqrt[4]{1}\\operatorname{cis} \\left( {\\frac{{\\tfrac{\\pi }{2}}}{4} + \\frac{{2\\pi }}{4}} \\right) = \\operatorname{cis} \\left( {\\frac{{5\\pi }}{8}} \\right)} \\\\<br \/>\n{k = 2:}&amp;{{w_2} = \\sqrt[4]{1}\\operatorname{cis} \\left( {\\frac{{\\tfrac{\\pi }{2}}}{4} + \\frac{{4\\pi }}{4}} \\right) = \\operatorname{cis} \\left( {\\frac{{9\\pi }}{8}} \\right)} \\\\<br \/>\n{k = 3:}&amp;{{w_3} = \\sqrt[4]{1}\\operatorname{cis} \\left( {\\frac{{\\tfrac{\\pi }{2}}}{4} + \\frac{{6\\pi }}{4}} \\right) = \\operatorname{cis} \\left( {\\frac{{13\\pi }}{8}} \\right)}<br \/>\n\\end{array}$$<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_9303' onClick='GTTabs_show(0,9303)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Determine: as cinco ra\u00edzes quintas de\u00a0$z = 1$; as quatro ra\u00edzes quartas de $z = i$. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":19608,"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-9303","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":2401,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat199.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9303","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=9303"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9303\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19608"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9303"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9303"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9303"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=9303"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}