{"id":2677,"date":"2022-05-02T18:56:46","date_gmt":"2022-05-02T16:56:46","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/zavedeni-i%c2%b2\/"},"modified":"2022-05-06T12:02:14","modified_gmt":"2022-05-06T10:02:14","slug":"zavedeni-i%c2%b2-1","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/zavedeni-i%c2%b2-1\/","title":{"rendered":"\u00davod do komplexn\u00edch \u010d\u00edsel- re\u00e1ln\u00e1 a komplexn\u00ed \u010d\u00e1st"},"content":{"rendered":"<p>Kolik zn\u00e1me \u010d\u00edseln\u00fdch obor\u016f \u010d\u00edsel?<\/p>\n<ul>\n<li>V\u00edme, \u017ee existuj\u00ed:<\/li>\n<\/ul>\n<ol>\n<li>P\u0159irozen\u00e1 \u010d\u00edsla<\/li>\n<li>Cel\u00e1 \u010d\u00edsla<\/li>\n<li>Racion\u00e1ln\u00ed \u010d\u00edsla<\/li>\n<li>Iracion\u00e1ln\u00ed \u010d\u00edsla<\/li>\n<li>Re\u00e1ln\u00e1 \u010d\u00edsla<\/li>\n<\/ol>\n<p>a nov\u011b tak\u00e9 <strong>KOMPLEXN\u00cd (IMAGIN\u00c1RN\u00cd) \u010c\u00cdSLA<\/strong>, kter\u00e1 zna\u010d\u00edme velk\u00fdm tiskac\u00edm p\u00edsmenem<strong> C<\/strong>.<\/p>\n<p>Co to ta komplexn\u00ed (imagin\u00e1rn\u00ed) \u010d\u00edsla jsou a kdy je vyu\u017eijeme?<\/p>\n<ul>\n<li>Komplexn\u00ed \u010d\u00edsla <strong>roz\u0161i\u0159uj\u00ed obor re\u00e1ln\u00fdch \u010d\u00edsel<\/strong>.<\/li>\n<li>Komplexn\u00ed \u010d\u00edsla se skl\u00e1daj\u00ed z RE\u00c1LN\u00c9 a IMAGIN\u00c1RN\u00cd \u010c\u00c1STI.<\/li>\n<li>Komplexn\u00ed \u010d\u00edslo zna\u010d\u00edme jako dvojici uspo\u0159\u00e1dan\u00fdch \u010d\u00edsel <em><strong>[x,y],<\/strong><\/em> kde <em><strong>x<\/strong><\/em> je <strong>re\u00e1ln\u00e1 \u010d\u00e1st<\/strong> a <strong><em>y<\/em><\/strong> je <strong>imagin\u00e1rn\u00ed \u010d\u00e1st<\/strong>.<\/li>\n<li>Re\u00e1lnou \u010d\u00e1st komplexn\u00edho \u010d\u00edsla zna\u010d\u00edme jako <strong>Re <em>x<\/em><\/strong> a imagin\u00e1rn\u00ed jako <strong>Im <em>x<\/em><\/strong>, pokud bychom tedy m\u011bli komplexn\u00ed \u010d\u00edslo<em><strong> a [x,y]<\/strong><\/em>, jeho re\u00e1ln\u00e1 \u010d\u00e1st by byla rovna <em><strong>x<\/strong><\/em> (<em><strong>Re a = x<\/strong><\/em>) a imagin\u00e1rn\u00ed by se rovnala <em><strong>y<\/strong><\/em> (<strong><em>Im a=y<\/em><\/strong>)<\/li>\n<\/ul>\n<p>N\u00e1zorn\u00fd p\u0159\u00edklad pro rozli\u0161en\u00ed re\u00e1ln\u00e9 a imagin\u00e1rn\u00ed \u010d\u00e1sti komplexn\u00edch \u010d\u00edsel. Ur\u010di re\u00e1lnou a komplexn\u00ed \u010d\u00e1st t\u011bchto \u010d\u00edsel:<\/p>\n<ul>\n<li>a=[0,2]<\/li>\n<\/ul>\n<p>Re a=0, Im a=2<\/p>\n<ul>\n<li>b [-3,0]<\/li>\n<\/ul>\n<p>Re b=-3, Im b=0<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-2677","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u00davod do komplexn\u00edch \u010d\u00edsel- re\u00e1ln\u00e1 a komplexn\u00ed \u010d\u00e1st | Studijni-svet.cz<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/zavedeni-i\u00b2-1\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u00davod do komplexn\u00edch \u010d\u00edsel- re\u00e1ln\u00e1 a komplexn\u00ed \u010d\u00e1st | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Kolik zn\u00e1me \u010d\u00edseln\u00fdch obor\u016f \u010d\u00edsel? V\u00edme, \u017ee existuj\u00ed: P\u0159irozen\u00e1 \u010d\u00edsla Cel\u00e1 \u010d\u00edsla Racion\u00e1ln\u00ed \u010d\u00edsla Iracion\u00e1ln\u00ed \u010d\u00edsla Re\u00e1ln\u00e1 \u010d\u00edsla a nov\u011b tak\u00e9 KOMPLEXN\u00cd (IMAGIN\u00c1RN\u00cd) \u010c\u00cdSLA, kter\u00e1 zna\u010d\u00edme velk\u00fdm tiskac\u00edm p\u00edsmenem C. Co to ta komplexn\u00ed (imagin\u00e1rn\u00ed) \u010d\u00edsla jsou a kdy je vyu\u017eijeme? Komplexn\u00ed \u010d\u00edsla roz\u0161i\u0159uj\u00ed obor re\u00e1ln\u00fdch \u010d\u00edsel. Komplexn\u00ed \u010d\u00edsla se skl\u00e1daj\u00ed z RE\u00c1LN\u00c9 a IMAGIN\u00c1RN\u00cd ... Read more\" \/>\n<meta property=\"og:url\" content=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/zavedeni-i\u00b2-1\/\" \/>\n<meta property=\"og:site_name\" content=\"Studijni-svet.cz\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/studijnisvet\/\" \/>\n<meta property=\"article:modified_time\" content=\"2022-05-06T10:02:14+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Odhadovan\u00e1 doba \u010dten\u00ed\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minuta\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/courses\\\/matematika-k-maturite\\\/lekce\\\/zavedeni-i%c2%b2-1\\\/\",\"url\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/courses\\\/matematika-k-maturite\\\/lekce\\\/zavedeni-i%c2%b2-1\\\/\",\"name\":\"\u00davod do komplexn\u00edch \u010d\u00edsel- re\u00e1ln\u00e1 a komplexn\u00ed \u010d\u00e1st | Studijni-svet.cz\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#website\"},\"datePublished\":\"2022-05-02T16:56:46+00:00\",\"dateModified\":\"2022-05-06T10:02:14+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/courses\\\/matematika-k-maturite\\\/lekce\\\/zavedeni-i%c2%b2-1\\\/#breadcrumb\"},\"inLanguage\":\"cs\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/courses\\\/matematika-k-maturite\\\/lekce\\\/zavedeni-i%c2%b2-1\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/courses\\\/matematika-k-maturite\\\/lekce\\\/zavedeni-i%c2%b2-1\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\u016f\",\"item\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Lekce\",\"item\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/lesson\\\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Matematika k maturit\u011b\",\"item\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/prehled\\\/matematika-k-maturite\\\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"\u00davod do komplexn\u00edch \u010d\u00edsel- re\u00e1ln\u00e1 a komplexn\u00ed \u010d\u00e1st\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#website\",\"url\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/\",\"name\":\"Akademie Studijni-svet.cz | Kurzy a podklady\",\"description\":\"Online akademie | Kurzy a podklady\",\"publisher\":{\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#organization\"},\"alternateName\":\"Akademie Studijni-svet.cz\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"cs\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#organization\",\"name\":\"Studijni-svet.cz\",\"url\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"cs\",\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/wp-content\\\/uploads\\\/2022\\\/01\\\/SS_logo-1.png\",\"contentUrl\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/wp-content\\\/uploads\\\/2022\\\/01\\\/SS_logo-1.png\",\"width\":66,\"height\":75,\"caption\":\"Studijni-svet.cz\"},\"image\":{\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/studijnisvet\\\/\",\"https:\\\/\\\/www.instagram.com\\\/studijnisvet.cz\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u00davod do komplexn\u00edch \u010d\u00edsel- re\u00e1ln\u00e1 a komplexn\u00ed \u010d\u00e1st | Studijni-svet.cz","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/zavedeni-i\u00b2-1\/","og_locale":"cs_CZ","og_type":"article","og_title":"\u00davod do komplexn\u00edch \u010d\u00edsel- re\u00e1ln\u00e1 a komplexn\u00ed \u010d\u00e1st | Studijni-svet.cz","og_description":"Kolik zn\u00e1me \u010d\u00edseln\u00fdch obor\u016f \u010d\u00edsel? V\u00edme, \u017ee existuj\u00ed: P\u0159irozen\u00e1 \u010d\u00edsla Cel\u00e1 \u010d\u00edsla Racion\u00e1ln\u00ed \u010d\u00edsla Iracion\u00e1ln\u00ed \u010d\u00edsla Re\u00e1ln\u00e1 \u010d\u00edsla a nov\u011b tak\u00e9 KOMPLEXN\u00cd (IMAGIN\u00c1RN\u00cd) \u010c\u00cdSLA, kter\u00e1 zna\u010d\u00edme velk\u00fdm tiskac\u00edm p\u00edsmenem C. Co to ta komplexn\u00ed (imagin\u00e1rn\u00ed) \u010d\u00edsla jsou a kdy je vyu\u017eijeme? Komplexn\u00ed \u010d\u00edsla roz\u0161i\u0159uj\u00ed obor re\u00e1ln\u00fdch \u010d\u00edsel. Komplexn\u00ed \u010d\u00edsla se skl\u00e1daj\u00ed z RE\u00c1LN\u00c9 a IMAGIN\u00c1RN\u00cd ... Read more","og_url":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/zavedeni-i\u00b2-1\/","og_site_name":"Studijni-svet.cz","article_publisher":"https:\/\/www.facebook.com\/studijnisvet\/","article_modified_time":"2022-05-06T10:02:14+00:00","twitter_card":"summary_large_image","twitter_misc":{"Odhadovan\u00e1 doba \u010dten\u00ed":"1 minuta"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/zavedeni-i%c2%b2-1\/","url":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/zavedeni-i%c2%b2-1\/","name":"\u00davod do komplexn\u00edch \u010d\u00edsel- re\u00e1ln\u00e1 a komplexn\u00ed \u010d\u00e1st | Studijni-svet.cz","isPartOf":{"@id":"https:\/\/studijni-svet.cz\/kurzy\/#website"},"datePublished":"2022-05-02T16:56:46+00:00","dateModified":"2022-05-06T10:02:14+00:00","breadcrumb":{"@id":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/zavedeni-i%c2%b2-1\/#breadcrumb"},"inLanguage":"cs","potentialAction":[{"@type":"ReadAction","target":["https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/zavedeni-i%c2%b2-1\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/zavedeni-i%c2%b2-1\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Dom\u016f","item":"https:\/\/studijni-svet.cz\/kurzy\/"},{"@type":"ListItem","position":2,"name":"Lekce","item":"https:\/\/studijni-svet.cz\/kurzy\/lesson\/"},{"@type":"ListItem","position":3,"name":"Matematika k maturit\u011b","item":"https:\/\/studijni-svet.cz\/kurzy\/prehled\/matematika-k-maturite\/"},{"@type":"ListItem","position":4,"name":"\u00davod do komplexn\u00edch \u010d\u00edsel- re\u00e1ln\u00e1 a komplexn\u00ed \u010d\u00e1st"}]},{"@type":"WebSite","@id":"https:\/\/studijni-svet.cz\/kurzy\/#website","url":"https:\/\/studijni-svet.cz\/kurzy\/","name":"Akademie Studijni-svet.cz | Kurzy a podklady","description":"Online akademie | Kurzy a podklady","publisher":{"@id":"https:\/\/studijni-svet.cz\/kurzy\/#organization"},"alternateName":"Akademie Studijni-svet.cz","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/studijni-svet.cz\/kurzy\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"cs"},{"@type":"Organization","@id":"https:\/\/studijni-svet.cz\/kurzy\/#organization","name":"Studijni-svet.cz","url":"https:\/\/studijni-svet.cz\/kurzy\/","logo":{"@type":"ImageObject","inLanguage":"cs","@id":"https:\/\/studijni-svet.cz\/kurzy\/#\/schema\/logo\/image\/","url":"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/01\/SS_logo-1.png","contentUrl":"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/01\/SS_logo-1.png","width":66,"height":75,"caption":"Studijni-svet.cz"},"image":{"@id":"https:\/\/studijni-svet.cz\/kurzy\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/studijnisvet\/","https:\/\/www.instagram.com\/studijnisvet.cz"]}]}},"_links":{"self":[{"href":"https:\/\/studijni-svet.cz\/kurzy\/wp-json\/wp\/v2\/lesson\/2677","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/studijni-svet.cz\/kurzy\/wp-json\/wp\/v2\/lesson"}],"about":[{"href":"https:\/\/studijni-svet.cz\/kurzy\/wp-json\/wp\/v2\/types\/lesson"}],"replies":[{"embeddable":true,"href":"https:\/\/studijni-svet.cz\/kurzy\/wp-json\/wp\/v2\/comments?post=2677"}],"version-history":[{"count":0,"href":"https:\/\/studijni-svet.cz\/kurzy\/wp-json\/wp\/v2\/lesson\/2677\/revisions"}],"wp:attachment":[{"href":"https:\/\/studijni-svet.cz\/kurzy\/wp-json\/wp\/v2\/media?parent=2677"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}