can I use the following formula for polar coordinates as well?

Question

Simpl asking, can I use the following formula for $\theta$ as we always do for an argument of a complex number $z=a+bi~$:

$$\theta=\tan^{-1}(b/a),~~a>0;~~~ \theta=\pi+\tan^{-1}(b/a),~~a<0$$

Thanks for any hints!