We can discuss $z$ in terms of circular coordinates.1
Let $z = (x, y) \in \C $. Since $z \in \R ^2$, we can identify $z$ with the polar coordinates of $(x, y)$ in the plane.
The argument of $z \in \C $ is $\tan^{-1}(\im{z}/\re{z})$. We denote the argument of $z$ by $\arg z$.2