{"id":2846,"date":"2022-05-14T18:06:39","date_gmt":"2022-05-14T16:06:39","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/odcitani-a-deleni-komplexnich-cisel\/"},"modified":"2022-05-14T19:26:06","modified_gmt":"2022-05-14T17:26:06","slug":"odcitani-a-deleni-komplexnich-cisel","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/odcitani-a-deleni-komplexnich-cisel\/","title":{"rendered":"Od\u010d\u00edt\u00e1n\u00ed a d\u011blen\u00ed komplexn\u00edch \u010d\u00edsel"},"content":{"rendered":"<p>Komplexn\u00ed \u010d\u00edsla se mezi sebou daj\u00ed samoz\u0159ejm\u011b tak\u00e9 od\u010d\u00edtat a d\u011blit. Proto\u017ee ji\u017e v\u00edme, jak vypadaj\u00ed opa\u010dn\u00e1 a p\u0159evr\u00e1cen\u00e1 \u010d\u00edsla k \u010d\u00edsl\u016fm komplexn\u00edm, m\u016f\u017eeme se vrhnout do od\u010d\u00edt\u00e1n\u00ed a d\u011blen\u00ed.<\/p>\n<p><strong>OD\u010c\u00cdT\u00c1N\u00cd KOMPLEXN\u00cdCH \u010c\u00cdSEL<\/strong><\/p>\n<ul>\n<li>p\u0159i od\u010d\u00edt\u00e1n\u00ed komplexn\u00edch \u010d\u00edsel pou\u017e\u00edv\u00e1me n\u00e1sleduj\u00edc\u00ed vzorec: $$x-y=(x_1-y_1)+(x_2-y_2)i$$<\/li>\n<li>s vyu\u017eit\u00edm tohoto vzorce nen\u00ed nijak slo\u017eit\u00e9 vypo\u010d\u00edtat n\u00e1sleduj\u00edc\u00ed p\u0159\u00edklad: $$(1+2i)-(1+4i)=(1-1)+(2-4)i=-2i$$<\/li>\n<\/ul>\n<p><strong>D\u011aLEN\u00cd KOMPLEXN\u00cdCH \u010c\u00cdSEL<\/strong><\/p>\n<ul>\n<li>p\u0159i d\u011blen\u00ed komplexn\u00edch \u010d\u00edsel mus\u00edme m\u00edt na pam\u011bti, \u017ee<strong> ve jmenovateli se mus\u00ed nach\u00e1zet re\u00e1ln\u00e9 \u010d\u00edslo<\/strong><\/li>\n<li>Jak doc\u00edlit toho, aby bylo ve jmenovateli re\u00e1ln\u00e9 \u010d\u00edslo? <strong>Zlomek roz\u0161\u00ed\u0159\u00edme \u010d\u00edslem komplexn\u011b sdru\u017een\u00fdm ke jmenovateli<\/strong>. Pro lep\u0161\u00ed pochopen\u00ed si poj\u010fme cel\u00fd postup d\u011blen\u00ed komplexn\u00edch \u010d\u00edsel uk\u00e1zat na vzorov\u00e9m p\u0159\u00edkladu.<\/li>\n<\/ul>\n<p>$$\\frac{3+5i}{2-i}$$<\/p>\n<p style=\"text-align: center\">prvn\u00ed krok spo\u010d\u00edv\u00e1 v tom, \u017ee zlomek roz\u0161\u00ed\u0159\u00edme komplexn\u011b sdru\u017een\u00fdm \u010d\u00edslem k \u010d\u00edslu <em>2-i<\/em><\/p>\n<p>$$\\frac{3+5i}{2-i}=\\frac{3+5i}{2-i}\\cdot{\\frac{2+i}{2+i}=\\frac{6+3i+10i+{5i}^{2}}{4+2i-2i-{i}^{2}}}=\\frac{6+13i-5}{4+1}=\\frac{1}{5}+\\frac{13}{5}i$$<\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-2846","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>Od\u010d\u00edt\u00e1n\u00ed a d\u011blen\u00ed komplexn\u00edch \u010d\u00edsel | 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\/odcitani-a-deleni-komplexnich-cisel\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Od\u010d\u00edt\u00e1n\u00ed a d\u011blen\u00ed komplexn\u00edch \u010d\u00edsel | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Komplexn\u00ed \u010d\u00edsla se mezi sebou daj\u00ed samoz\u0159ejm\u011b tak\u00e9 od\u010d\u00edtat a d\u011blit. Proto\u017ee ji\u017e v\u00edme, jak vypadaj\u00ed opa\u010dn\u00e1 a p\u0159evr\u00e1cen\u00e1 \u010d\u00edsla k \u010d\u00edsl\u016fm komplexn\u00edm, m\u016f\u017eeme se vrhnout do od\u010d\u00edt\u00e1n\u00ed a d\u011blen\u00ed. OD\u010c\u00cdT\u00c1N\u00cd KOMPLEXN\u00cdCH \u010c\u00cdSEL p\u0159i od\u010d\u00edt\u00e1n\u00ed komplexn\u00edch \u010d\u00edsel pou\u017e\u00edv\u00e1me n\u00e1sleduj\u00edc\u00ed vzorec: $$x-y=(x_1-y_1)+(x_2-y_2)i$$ s vyu\u017eit\u00edm tohoto vzorce nen\u00ed nijak slo\u017eit\u00e9 vypo\u010d\u00edtat n\u00e1sleduj\u00edc\u00ed p\u0159\u00edklad: $$(1+2i)-(1+4i)=(1-1)+(2-4)i=-2i$$ D\u011aLEN\u00cd KOMPLEXN\u00cdCH \u010c\u00cdSEL ... 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Proto\u017ee ji\u017e v\u00edme, jak vypadaj\u00ed opa\u010dn\u00e1 a p\u0159evr\u00e1cen\u00e1 \u010d\u00edsla k \u010d\u00edsl\u016fm komplexn\u00edm, m\u016f\u017eeme se vrhnout do od\u010d\u00edt\u00e1n\u00ed a d\u011blen\u00ed. OD\u010c\u00cdT\u00c1N\u00cd KOMPLEXN\u00cdCH \u010c\u00cdSEL p\u0159i od\u010d\u00edt\u00e1n\u00ed komplexn\u00edch \u010d\u00edsel pou\u017e\u00edv\u00e1me n\u00e1sleduj\u00edc\u00ed vzorec: $$x-y=(x_1-y_1)+(x_2-y_2)i$$ s vyu\u017eit\u00edm tohoto vzorce nen\u00ed nijak slo\u017eit\u00e9 vypo\u010d\u00edtat n\u00e1sleduj\u00edc\u00ed p\u0159\u00edklad: $$(1+2i)-(1+4i)=(1-1)+(2-4)i=-2i$$ D\u011aLEN\u00cd KOMPLEXN\u00cdCH \u010c\u00cdSEL ... 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