Find all solutions to:

$\displaystyle z^i=1$

Can someone give me the method to solve this?

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- Feb 24th 2010, 12:49 PMpaupsersStuck on super-simple complex problem
Find all solutions to:

$\displaystyle z^i=1$

Can someone give me the method to solve this? - Feb 24th 2010, 01:20 PMLaurent
The equation rewrites $\displaystyle e^{i \log z}=1$ (which may depend on the determination of the complex logarithm), so you are first reduced to solving $\displaystyle e^{w}=1$ for $\displaystyle w\in\mathbb{C}$, 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.