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Math Help - Complex Numbers

  1. #1
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    Complex Numbers

    Hi guys, hopefully this is in the correct thread.

    I have two questions that are bugging me...:

    1) Express the following complex number in the exponential polar form: (2-2 x sqrt(3) x i)^13

    2) Using the complex exponential, express cos(4theda) in terms of cos(theda).

    Any help would be greatly appreciated!

    Thanks -
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  2. #2
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    Re: Complex Numbers

    Quote Originally Posted by Jonathancrowden774 View Post
    1) Express the following complex number in the exponential polar form: (2-2 x sqrt(3) x i)^13

    2) Using the complex exponential, express cos(4theda) in terms of cos(theda).
    |2-2\sqrt3i|=4 and \text{Arg}(2-2\sqrt3i)=\frac{-\pi}{3}

    \cos(t)=\frac{e^{it}+e^{-it}}{2}
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  3. #3
    Junior Member ignite's Avatar
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    Re: Complex Numbers

    Quote Originally Posted by Plato View Post
    |2-2\sqrt3i|=4 and \text{Arg}(2-2\sqrt3i)=\frac{-\pi}{3}

    \cos(t)=\frac{e^{it}+e^{-it}}{2}
    I would like to add for the second part,
    e^{4i\theta}={(e^{i\theta})}^4}\Rightarrow cos(4\theta)+isin(4\theta)={(cos\theta+isin\theta)  }^4

    Expand the right hand side using Binomial Expansion and then equate the real parts to get the value of cos4\theta.
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