Thread: Stuck on super-simple complex problem

1. Stuck on super-simple complex problem

Find all solutions to:

$z^i=1$

Can someone give me the method to solve this?

2. Originally Posted by paupsers
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.