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Thread: Stuck on super-simple complex problem

  1. February 24th 2010, 12:49 PM #1
    paupsers
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    Stuck on super-simple complex problem

    Find all solutions to:

    z^i=1

    Can someone give me the method to solve this?
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  2. February 24th 2010, 01:20 PM #2
    Laurent
    Laurent is offline
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    Quote Originally Posted by paupsers View Post
    Find all solutions to:

    z^i=1

    Can someone give me the method to solve this?
    The equation rewrites e^{i \log z}=1 (which may depend on the determination of the complex logarithm), so you are first reduced to solving e^{w}=1 for w\in\mathbb{C}, which is a classic one (decompose w in real and complex parts if you don't know the answer already).
    You'll find that the final answer actually doesn't depend on the determination of the logarithm.
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