Complex numbers polar form change I have a pretty straight forward question. 
Change $z = (-1+i\sqrt3)^{2017}$ to $a+bi$ $\;$ form & polar form. Where $i = \sqrt{-1}$. 
So i want to change it to $z = re^{iv}$. 
$r$ is easy to calculate. $r = \sqrt4 = 2$. 
However the angle is where im struggeling. 
I know all the "standard" angles with components like:  $\frac{\sqrt3}2, \frac12, \frac1{\sqrt2}$. 
However now we have $\frac{\sqrt3}{-1}$. How do you tackle this type of question?

$z = (-1+i\sqrt3)^{2017} = (2\omega)^{2017}$, where $\omega = \dfrac{-1+i\sqrt3}{2}$ is the third root of unity.  ($v = \arctan(\sqrt3/(-1)) = \dfrac{2\pi}{3}$), so $$z = 2^{2017} \omega^{2017} = 2^{2017} = 2^{2017} e^{2\pi/3} \\ = 2^{2017} \, \frac{-1+i\sqrt3}{2} = -2^{2016} + i \, 2^{2016}\sqrt3.$$
