Convert polar complex number to cartesian

Question

I need to convert $e^{1+i(\pi/4)}$ into Cartesian form. Normally, I would use r and the arg to convert to $r(\cos\theta + i \sin\theta$) and I would be fine to go from there. The fact that there is a $+1$ in the exponent as well is throwing me off and I don't know where to start.

Answer 1

Note that $$e^{1+i(\pi/4)}= e e^{i(\pi/4)} = e(\cos (\pi/4)+ i \sin (\pi/4))$$

Answer 2

In general $e^z = e^{\Re(z) + i\Im(z)} = e^{\Re(z)}(\cos\Im(z) + i\sin \Im (z))$.

You should be able to apply this to your case.