I've stuck on a basic exercise.

I must find all complex numbers $\displaystyle z$ such that $\displaystyle \arg (e^z)=\frac{\pi}{4}$.

Which is equivalent to say that $\displaystyle \arg (\underbrace{e^x \cos y}_{a} + i \underbrace {e^x \sin y}_{b} )= \frac{\pi}{4}$.

I remember a long time ago I've learned a formula where $\displaystyle a$, $\displaystyle b$ and $\displaystyle r$, the module of $\displaystyle z$ were involved that could solve for an argument of $\displaystyle z$. This is the only way that comes to my mind right now about how to solve the problem.