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Teoirim De Moivre ( cos  + i sin  ) n = cosn  + i sinn 

Teoirim De Moivre ( cos  + i sin  ) n = cosn  + i sinn . Le Cruthú: (cos  + i sin  ) n = cosn  + i sinn  n  Z. Cruthú: Glac leis gur fíor é i gcás n = k Dá réir sin (cos  + i sin  ) k = cosk  + i sink . Cruthaigh go bhfuil sé fíor i gcás n=k+1.

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Teoirim De Moivre ( cos  + i sin  ) n = cosn  + i sinn 

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  1. Teoirim De Moivre(cos + i sin)n = cosn + i sinn Le Cruthú: (cos + i sin )n = cosn + i sinn n  Z Cruthú: Glac leis gur fíor é i gcás n = k Dá réir sin(cos + i sin)k= cosk + i sink Cruthaigh go bhfuil sé fíor i gcás n=k+1 (cos + i sin)k+1 = (cos + i sin)k (cos + i sin)1 = (cosk + i sink)(cos + i sin)1 = coskcos + icosksin + i sinkcos + i2sink sin  = cos kcos - sink sin + i(cosk sin + sin k cos ) =cos(k+1) + i sin(k+1)  Is fíor é i gcás n = k, Is fíor é i gcás n =k+1 Ach is fíor é i gcás n = 1 mar tá (Cos +i sin )1=cos +i sin  Dá réir sin leis an Ionduchtú is fíor é i gcás n , n = Z+ (cos + i sin)n = cosn + i sinn Cóipcheart Foireann Fhorbartha Thionscadal Mata 2012

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