{"id":10454,"date":"2025-07-15T13:34:50","date_gmt":"2025-07-15T13:34:50","guid":{"rendered":"https:\/\/functiontranslator.com\/modul-liczby-zesp\/"},"modified":"2021-02-26T05:11:19","modified_gmt":"2021-02-26T05:11:19","slug":"imabs","status":"publish","type":"post","link":"https:\/\/functiontranslator.com\/pl\/imabs\/","title":{"rendered":"MODU\u0141.LICZBY.ZESP"},"content":{"rendered":"

Syntaktyka i Opis Funkcji<\/h2>\n

W Excel, funkcja MODU\u0141.LICZBY.ZESP, znana r\u00f3wnie\u017c jako IMABS w Google Sheets, pozwala na obliczenie modu\u0142u liczby zespolonej. Liczba zespolona jest zapisywana jako „x + yi” lub „x + yj”, gdzie „x” reprezentuje cz\u0119\u015b\u0107 rzeczywist\u0105, a „y” cz\u0119\u015b\u0107 urojon\u0105.<\/p>\n

Syntaktyka funkcji w Excel:<\/strong><\/p>\n

<code>MODU\u0141.LICZBY.ZESP(liczba_zespolona)<\/code><\/code><\/pre>\n
Syntaktyka funkcji w Google Sheets:<\/strong><\/p>\n
<code>IMABS(liczba_zespolona)<\/code><\/code><\/pre>\n
Liczba zespolona powinna by\u0107 podana jako argument w cudzys\u0142owie, na przyk\u0142ad „3+4i”.<\/p>\n
Przyk\u0142ad podstawowego stosowania<\/h2>\n
Rozwa\u017cmy liczb\u0119 zespolon\u0105 „3+4i”. Mo\u017cemy obliczy\u0107 jej modu\u0142 korzystaj\u0105c z obu funkcji:<\/p>\n
    \n
  • W Excelu: =MODU\u0141.LICZBY.ZESP(\"3+4i\")<\/code><\/li>\n
  • W Google Sheets: =IMABS(\"3+4i\")<\/code><\/li>\n<\/ul>\n
    W obu przypadkach wynik wyniesie 5, co wynika z obliczenia √(x^2 + y^2).<\/p>\n
    Zastosowania praktyczne<\/h2>\n
    Analyzowanie sygna\u0142\u00f3w<\/h2>\n
    Praca z sygna\u0142ami elektrycznymi zawieraj\u0105cymi sk\u0142adowe zespolone cz\u0119sto wymaga obliczenia modu\u0142u. Na przyk\u0142ad, dla sygna\u0142u „2+5i”, modu\u0142 mo\u017ce by\u0107 interpretowany jako amplituda sygna\u0142u:<\/p>\n
    <code>=MODU\u0141.LICZBY.ZESP(\"2+5i\") \/\/ wynik \u2248 5,385<\/code><\/code><\/pre>\n
    Obliczanie odleg\u0142o\u015bci w przestrzeni zespolonej<\/h2>\n
    W matematyce i fizyce istnieje potrzeba obliczenia odleg\u0142o\u015bci mi\u0119dzy punktami w przestrzeni zespolonej. Na przyk\u0142ad, odleg\u0142o\u015b\u0107 mi\u0119dzy punktami „1+2i” i „4+6i” mo\u017cna obliczy\u0107 jako modu\u0142 r\u00f3\u017cnicy tych liczb:<\/p>\n
    <code>=MODU\u0141.LICZBY.ZESP(\"1+2i\" - \"4+6i\") \/\/ Wynik to √((-3)^2 + (-4)^2) = 5<\/code><\/code><\/pre>\n
    W powy\u017cszym przyk\u0142adzie najpierw wykonujemy odejmowanie dw\u00f3ch liczb zespolonych, a nast\u0119pnie obliczamy modu\u0142 wynikowego wyra\u017cenia.<\/p>\n","protected":false},"excerpt":{"rendered":"
    Zwraca warto\u015b\u0107 bezwzgl\u0119dn\u0105 (modu\u0142) liczby zespolonej<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[429],"tags":[],"class_list":["post-10454","post","type-post","status-publish","format-standard","hentry","category-inzynierskie"],"acf":[],"yoast_head":"\nFunkcja IMABS (MODU\u0141.LICZBY.ZESP) w Excelu \u2013 jak dzia\u0142a, przyk\u0142ady u\u017cycia i sk\u0142adnia<\/title>\n<meta name=\"description\" content=\"Opis funkcji IMABS (MODU\u0141.LICZBY.ZESP) w Excelu. 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