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Math Help - DeMoivre's Theorem

  1. #1
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    DeMoivre's Theorem

    Let z= 1/2+ square root of 3 over 2i
    Perform the computation using DeMoivre's theorem and explain why this theorem makes the computation easier
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    Re: DeMoivre's Theorem

    computation of what?
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    Re: DeMoivre's Theorem

    computation involving z using DeMoivre's Theorem
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    Re: DeMoivre's Theorem

    It's not even clear what z is. Do you mean \frac{1}{2}+\frac{\sqrt{3}}{2}i?

    If so what do you want to do with it?
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    Re: DeMoivre's Theorem

    Quote Originally Posted by derek1008 View Post
    Let z= 1/2+ square root of 3 over 2i
    Perform the computation using DeMoivre's theorem and explain why this theorem makes the computation easier
    \frac{1}{2}+\frac{\sqrt{3}}{2}i=\exp\left(\frac{i\  pi}{3}\right).

    Now what do you want done?
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    Re: DeMoivre's Theorem

    The question asks to identify a computation involving z that can be performed using DeMoivre's Theorem.
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    Re: DeMoivre's Theorem

    Quote Originally Posted by derek1008 View Post
    The question asks to identify a computation involving z that can be performed using DeMoivre's Theorem.

    If \alpha\in\mathbb{R}, a real number, then if
    z=\frac{1}{2}+\frac{\sqrt{3}}{2}i=\exp\left(\frac{  i\pi}{3}\right) we have
    z^{\alpha}=\exp\left(\frac{i\pi\alpha}{3}\right).
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    Re: DeMoivre's Theorem

    Quote Originally Posted by derek1008 View Post
    The question asks to identify a computation involving z that can be performed using DeMoivre's Theorem.
    ok ...

    z = r(\cos{\theta} + i \sin{\theta})

    if z = \frac{1}{2} + \frac{\sqrt{3}}{2} i , then r = 1 and \theta = \frac{\pi}{3}
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