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Homework Statement
I want to prove something that seems trivial at first:
[itex] (z^m)^{1/n}=(z^{1/n})^m [/itex], where m and n don't have a common divisor.
The Attempt at a Solution
When I'm using [itex] z=re^{i\theta}[/itex], I arrive that above is true if and only if the following is true:
[itex] e^{ \frac{2\pi \theta mk}{n}}=e^{\frac{2\pi \theta k}{n}} [/itex]
and this confuses me.