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Thread: Complex numbers powers can any one help ...

  1. #1
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    Complex numbers powers can any one help ...

    Let z=3(cos(-1/3*pi)+i sin(-1/3*pi))
    What is the modulus of z^3
    |z^3| =
    I'm not quite sure how to go about this can anyone help please ,I struggle with powers of complex numbers .
    Thanks
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  2. #2
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    Re: Complex numbers powers can any one help ...

    Use de Moivre's theorem:

    If z = r(cos (A) + i sin (A))  then  z^n =  r^n(cos (nA) + i sin (nA)).
    Thanks from bee77
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    Re: Complex numbers powers can any one help ...

    ahh right ,I'd have to find R first right ?
    I know on the cartesian plane its |z| = sqrt *a^2+b^2 ...how about in polar form how would I find R ....not sure if my answers right or not ,Thanks
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    Re: Complex numbers powers can any one help ...

    Quote Originally Posted by bee77 View Post
    ahh right ,I'd have to find R first right ?
    I know on the cartesian plane its |z| = sqrt *a^2+b^2 ...how about in polar form how would I find R ....not sure if my answers right or not ,Thanks
    You've been given the complex number in polar form , ie r(cos(A) + i sin(A)) so r = 3
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