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Math Help - induction proof of de moivres formula

  1. #1
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    induction proof of de moivres formula

    Is this correct and enough proof
    (cosx+isinx)^n=cos(nx)+isinx is true so i put 1 and its true now ima prove for
    S(k+1) = (Cosx+isinx)^k+1= (Cosx+isinx)^k(cosx+isinx) now we can rewrite that ^k with a formula i cant remember as
    (coskx+isinkx)(cosx+isinx)
    and now i foctour out cos x and sin x
     Cos x ( k+1) + iSinx(k+1)
    is this enough
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  2. #2
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    Re: induction proof of de moivres formula

    You "can't remember"? You just wrote it two lines above!
    For n a positive integer, yes, that will be a valid proof once you use trig identities to show how you got from (cos(kx)+ isin(kx))(cos(x)+ i sin(x)) to cos((k+1)x)+ i sin((k+1)x).

    DeMoivre's formula is true for n any number, of course, not just positive integers. It would think the simplest way to prove it is to use the fact that cos(x)+ i sin(x)= e^{ix}.
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