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Math Help - DeMoivre's Theorem Problem

  1. #1
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    DeMoivre's Theorem Problem

    Any Help will be Appreciated

    DeMoivre's Theorem is this ( i is the imaginary unit):

    (cos(x) + isin(x)) ^ n = con(nx) + isin(nx)

    Let n = 3, and deduce the following

    sin(3x) = 3 ((cos(x)) ^ 2) (sin(x)) - (sin(x) ^ 3)

    and

    cos(3x) = (cos(x) ^ 3) - 3 (cos(x)) (sin(x) ^ 2)

    I can simplyify to the point where I need to use the other equation to prove the one I'm on. However, I can't use that unless I have already proved one of them first.
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  2. #2
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    Quote Originally Posted by hashshashin715 View Post
    Any Help will be Appreciated

    DeMoivre's Theorem is this ( i is the imaginary unit):

    (cos(x) + isin(x)) ^ n = con(nx) + isin(nx)

    Let n = 3, and deduce the following

    sin(3x) = 3 ((cos(x)) ^ 2) (sin(x)) - (sin(x) ^ 3)

    and

    cos(3x) = (cos(x) ^ 3) - 3 (cos(x)) (sin(x) ^ 2)

    I can simplyify to the point where I need to use the other equation to prove the one I'm on. However, I can't use that unless I have already proved one of them first.

    Write \left(\cos x + i\sin x\right)^3 in two ways: first, using de Moivre theorem , and second using the binomial expansion (a+b)^3=a^3+3a^2b+3ab^2+b^3 (pay attention to the imaginary unit here!). Finally, just equal real and imaginar parts in both expressions.

    Tonio
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  3. #3
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    Ok, Thanks
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