How to calculate $\theta$ when we know $\tan \theta$. Hej
I'm having difficulties calculating the angle given the tangent.
Example:
In a homework assignement I'm to express a complex variable $z = \sqrt{3} -i$ in polar form. I know how to solve this except for when I get to calculating the angle $\theta$.
I know that $\tan \theta = -\frac{1}{\sqrt{3}}$  but I do not know how to continue and compute the angle from that.

You can find the reference angle by disregarding the sign , you still need to figure out which quadrant you are in (which is easy) so you can add or subtract the reference angle accordingly
$$ \theta_R = tan^{-1} \frac{1}{ \sqrt{3}} $$
$$ \theta_R = \frac{ \pi}{6} $$
We are in the 4th quadrant so ,
$$ \theta = 2 \pi - \frac{ \pi}{6} = \frac{ 11 \pi}{6} $$
Now , if you need more working angles just add integer multiples of  $ 2 \pi $
