Finding complex roots, specifically theta

Question

I'm trying to find the roots for $$(-4+4i)^{^\frac{1}{5})}$$ I have the formula, $$\sqrt[n]{z}=\sqrt[n]{r}\left(\cos\frac{\theta+2\pi k}{n}+i\sin \frac{\theta +2 \pi k}{n}\right)$$ where k=0, 1, ..., n-1. So then, $$r=\sqrt{(-4)^2 +4^2}=\sqrt{32}$$ $$\sqrt[5]{\sqrt{32}}\left(\cos\frac{\theta+2\pi k}{5}+i\sin \frac{\theta +2 \pi k}{5}\right)$$ What I do not get is how to find theta.

Answer 1

Hint: $-4+4i=4\sqrt2\left(-\frac{\sqrt2}2+\frac{\sqrt2}2i\right)$.

Answer 2

HINT

Recall that given $z=iy$ we have for $x\neq 0$

$$\tan \theta = \frac y x \implies \begin{cases}x>0\quad\theta = \arctan \left(\frac y x\right)\\\\x<0\quad \theta = \pi +\arctan \left(\frac y x\right)\end {cases}$$