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Math Help - Complex Numbers: How to solve these kind of tasks?

  1. #1
    Newbie Flamuri's Avatar
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    Complex Numbers: How to solve these kind of tasks?

    I'm having problems to solve these kind of tasks with powers - like:

    \left ( \frac{\sqrt{3}-i}{1+i} \right )^{24}

    Or

    \frac{(\sqrt{3}-i)^{13}}{(1+i)^{16}} + \frac{(\sqrt{3}+i)^{13}}{(1-i)^{16}}

    I try with racitonalizing but i don't get much. Would appreciate any kind of help.
    Thanks,

    Flamuri
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  2. #2
    MHF Contributor

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    Re: Complex Numbers: How to solve these kind of tasks?

    Quote Originally Posted by Flamuri View Post
    \left ( \frac{\sqrt{3}-i}{1+i} \right )^{24}
    First use polar form.
    \sqrt{3}-i=2\exp\left(\frac{-\pi i}{6}\right)~\&~1+i=\sqrt{2}\exp\left(\frac{\pi i}{4}\right)

    Now it is easy to raise those to 24th power.
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