how to calculate the angle(s) of $\ -\sqrt{2i}$

Question

So $\tan \phi = \frac yx $

But my $\ x = 0$ , so how do I find the respective angle?

The context is me trying to find the roots of $\ -\sqrt{2i}$

It should be something to the respect of $\ (1+i)$ and $\ (-1-i)$ or

$\ \sqrt{2} e^{i \cdot \frac \pi 4 }$ and $\ \sqrt{2} e^{3i \cdot \frac \pi 4 }$

but i don't really get how I'm supposed to get there without finding $\ \phi $ since for the squareroots it's also it's $\ \sqrt{r} e^{i \frac \phi 2 }$

I feel like I'm missing a vital bit here.

Answer 1

HINT

• write $2i$ in exponential form that is $2i=2e^{i\frac{\pi}2}$
• calculate $\sqrt{2i}$ that is $\sqrt 2 e^{i\frac{\pi}4} \quad \sqrt 2 e^{i\frac{5\pi}4}$
• take $-\sqrt{2i}$