complex numbers - How can I prove this equation?

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.