{"id":9205,"date":"2012-05-21T17:54:18","date_gmt":"2012-05-21T16:54:18","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=9205"},"modified":"2021-12-29T13:33:47","modified_gmt":"2021-12-29T13:33:47","slug":"escreva-z-na-forma-trigonometrica","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=9205","title":{"rendered":"Escreva $z$ na forma trigonom\u00e9trica"},"content":{"rendered":"<p><ul id='GTTabs_ul_9205' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_9205' class='GTTabs_curr'><a  id=\"9205_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_9205' ><a  id=\"9205_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_9205'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Escreva $z$ na forma trigonom\u00e9trica:<\/p>\n<ol>\n<li>$z = 1 &#8211; i\\sqrt 3 $<\/li>\n<li>$z =\u00a0 &#8211; 1 + i$<\/li>\n<li>$z =\u00a0 &#8211; 5$<\/li>\n<li>$z = 3i$<\/li>\n<li>$z = \\frac{1}{3} + \\frac{1}{3}i$<\/li>\n<li>$z =\u00a0 &#8211; \\sqrt 2\u00a0 &#8211; \\sqrt 6 i$<\/li>\n<li>$z = \\frac{4}{{1 &#8211; i\\sqrt 3 }}$<\/li>\n<li>$z = \\frac{2}{{\\sqrt 6\u00a0 &#8211; i\\sqrt 2 }}$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_9205' onClick='GTTabs_show(1,9205)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_9205'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{1 &#8211; i\\sqrt 3 } \\\\<br \/>\n{}&amp; = &amp;{2\\left( {\\frac{1}{2} &#8211; \\frac{{\\sqrt 3 }}{2}i} \\right)} \\\\<br \/>\n{}&amp; = &amp;{2\\operatorname{cis} \\left( { &#8211; \\frac{\\pi }{3}} \\right)}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{ &#8211; 1 + i} \\\\<br \/>\n{}&amp; = &amp;{\\sqrt 2 \\left( { &#8211; \\frac{{\\sqrt 2 }}{2} + \\frac{{\\sqrt 2 }}{2}i} \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\sqrt 2 \\operatorname{cis} \\left( {\\frac{{3\\pi }}{4}} \\right)}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{ &#8211; 5} \\\\<br \/>\n{}&amp; = &amp;{5\\operatorname{cis} \\pi }<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{3i} \\\\<br \/>\n{}&amp; = &amp;{3\\operatorname{cis} \\frac{\\pi }{2}}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{\\frac{1}{3} + \\frac{1}{3}i} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{\\sqrt 2 }}{3}\\left( {\\frac{{\\sqrt 2 }}{2} + \\frac{{\\sqrt 2 }}{2}i} \\right)} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{\\sqrt 2 }}{3}\\operatorname{cis} \\frac{\\pi }{4}}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{ &#8211; \\sqrt 2\u00a0 &#8211; \\sqrt 6 i} \\\\<br \/>\n{}&amp; = &amp;{2\\sqrt 2 \\left( { &#8211; \\frac{1}{2} &#8211; \\frac{{\\sqrt 3 }}{2}i} \\right)} \\\\<br \/>\n{}&amp; = &amp;{2\\sqrt 2 \\operatorname{cis} \\left( {\\frac{{4\\pi }}{3}} \\right)}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{\\frac{4}{{1 &#8211; i\\sqrt 3 }}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{4\\operatorname{cis} \\left( 0 \\right)}}{{2\\left( {\\frac{1}{2} &#8211; \\frac{{\\sqrt 3 }}{2}i} \\right)}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{4\\operatorname{cis} \\left( 0 \\right)}}{{2\\operatorname{cis} \\left( { &#8211; \\frac{\\pi }{3}} \\right)}}} \\\\<br \/>\n{}&amp; = &amp;{2\\operatorname{cis} \\left( {0 + \\frac{\\pi }{3}} \\right)} \\\\<br \/>\n{}&amp; = &amp;{2\\operatorname{cis} \\frac{\\pi }{3}}<br \/>\n\\end{array}$$<\/li>\n<li>Ora,<br \/>\n$$\\begin{array}{*{20}{l}}<br \/>\nz&amp; = &amp;{\\frac{2}{{\\sqrt 6\u00a0 &#8211; i\\sqrt 2 }}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{2\\operatorname{cis} \\left( 0 \\right)}}{{2\\sqrt 2 \\left( {\\frac{{\\sqrt 3 }}{2} &#8211; \\frac{1}{2}i} \\right)}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{2\\operatorname{cis} \\left( 0 \\right)}}{{2\\sqrt 2 \\operatorname{cis} \\left( { &#8211; \\frac{\\pi }{6}} \\right)}}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{2}{{2\\sqrt 2 }}\\operatorname{cis} \\frac{\\pi }{6}} \\\\<br \/>\n{}&amp; = &amp;{\\frac{{\\sqrt 2 }}{2}\\operatorname{cis} \\frac{\\pi }{6}}<br \/>\n\\end{array}$$<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_9205' onClick='GTTabs_show(0,9205)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Escreva $z$ na forma trigonom\u00e9trica: $z = 1 &#8211; i\\sqrt 3 $ $z =\u00a0 &#8211; 1 + i$ $z =\u00a0 &#8211; 5$ $z = 3i$ $z = \\frac{1}{3} + \\frac{1}{3}i$ $z&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19179,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,310],"tags":[427,314,18],"series":[],"class_list":["post-9205","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-forma-trigonometrica","tag-numeros-complexos"],"views":1240,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat70.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9205","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=9205"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/9205\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9205"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9205"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9205"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=9205"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}