{"id":10468,"date":"2025-07-15T13:34:50","date_gmt":"2025-07-15T13:34:50","guid":{"rendered":"https:\/\/functiontranslator.com\/potega-liczby-zesp\/"},"modified":"2021-02-26T05:18:24","modified_gmt":"2021-02-26T05:18:24","slug":"impower","status":"publish","type":"post","link":"https:\/\/functiontranslator.com\/pl\/impower\/","title":{"rendered":"POT\u0118GA.LICZBY.ZESP"},"content":{"rendered":"

Wprowadzenie<\/h2>\n

Funkcja IMPOWER<\/strong> w Microsoft Excel oraz POT\u0118GA.LICZBY.ZESP<\/strong> w Google Tablicach umo\u017cliwiaj\u0105 obliczenie pot\u0119gi liczby zespolonej. Zar\u00f3wno narz\u0119dzia w Excelu, jak i Google Sheets oferuj\u0105 podobne funkcjonalno\u015bci przy pracy z liczbami zespolonymi, cho\u0107 ich sk\u0142adnia mo\u017ce nieco si\u0119 r\u00f3\u017cni\u0107.<\/p>\n

Syntaktyka funkcji<\/h2>\n

Syntaktyka funkcji prezentuje si\u0119 nast\u0119puj\u0105co:<\/p>\n

 IMPOWER(kompleksna_liczba, pot\u0119ga) <\/code><\/pre>\n
    \n
  • kompleksna_liczba<\/strong> – Tekstowo przedstawiona liczba zespolona, dla kt\u00f3rej chcemy obliczy\u0107 pot\u0119g\u0119, na przyk\u0142ad „3+4i”.<\/li>\n
  • pot\u0119ga<\/strong> – Liczba ca\u0142kowita okre\u015blaj\u0105ca wyk\u0142adnik pot\u0119gi.<\/li>\n<\/ul>\n
    Przyk\u0142ad:<\/p>\n
     =IMPOWER(\"3+2i\", 2) <\/code><\/pre>\n
    Wynik: 5+12i<\/strong><\/p>\n
    Zastosowanie w praktyce<\/h2>\n
    Oto dwa praktyczne przyk\u0142ady u\u017cycia funkcji IMPOWER<\/strong>.<\/p>\n
    Przyk\u0142ad 1: Obliczanie impedancji w obwodach elektrycznych<\/h2>\n
    W elektronice cz\u0119sto mierzy si\u0119 ca\u0142kowit\u0105 impedancj\u0119 obwod\u00f3w z elementami RLC, gdzie ka\u017cdy z element\u00f3w ma swoj\u0105 impedancj\u0119 wyra\u017con\u0105 jako liczba zespolona. Przyk\u0142adem mo\u017ce by\u0107 obw\u00f3d LC, gdzie impedancja induktora (L) wynosi j2\u03a9, a kondensatora (C) – j-1\u03a9. Obliczaj\u0105c sum\u0119 tych impedancji a nast\u0119pnie kwadrat sumy, otrzymujemy impedancj\u0119 wej\u015bciow\u0105 obwodu.<\/p>\n
     =IMPOWER(\"j2-j1\", 2) <\/code><\/pre>\n
    Wynik: -3-2j<\/strong>, co odpowiada kwadratowej warto\u015bci impedancji tego uk\u0142adu.<\/p>\n
    Przyk\u0142ad 2: Analiza sygna\u0142\u00f3w sinusoidalnych<\/h2>\n
    In\u017cynierowie analizuj\u0105cy skomplikowane sygna\u0142y cz\u0119sto rozk\u0142adaj\u0105 je na sk\u0142adowe sinusoidalne. Przy rozwa\u017caniu sygna\u0142u opisanego przez zespolon\u0105 funkcj\u0119 „1+i” podniesion\u0105 do trzeciej pot\u0119gi, mo\u017cemy obserwowa\u0107 zmiany fazy i amplitudy sygna\u0142u.<\/p>\n
     =IMPOWER(\"1+i\", 3) <\/code><\/pre>\n
    Wynik: -2+2i<\/strong>, ukazuj\u0105cy, jak parametry sygna\u0142u ewoluuj\u0105 w wyniku tej operacji.<\/p>\n","protected":false},"excerpt":{"rendered":"
    Zwraca warto\u015b\u0107 liczby zespolonej podniesionej do pot\u0119gi ca\u0142kowitej<\/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-10468","post","type-post","status-publish","format-standard","hentry","category-inzynierskie"],"acf":[],"yoast_head":"\nFunkcja IMPOWER (POT\u0118GA.LICZBY.ZESP) w Excelu \u2013 jak dzia\u0142a, przyk\u0142ady u\u017cycia i sk\u0142adnia<\/title>\n<meta name=\"description\" content=\"Opis funkcji IMPOWER (POT\u0118GA.LICZBY.ZESP) w Excelu. 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