My prof put this equation on the board, without any kind of explanation or proof. When I asked him for one, he didn't really give me a solid answer.
$$w = r(\cos \theta + i\sin \theta)$$
Then
$w^n = r^n(\cos n\theta + i\sin n\theta)$ for $n \in \mathbb{R}$
I would try to prove this, but it's a bit beyond me considering I learn't what a complex number is a week ago. Please don't use Euler's Theorem.
EDIT: I ended up using induction since the formula is not valid for non-integers.
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