I've been trying to solve this problem for a couple of days but i can´t find a convincent solution. The problem says:
Let $f(z)=\exp(z)\cos(z)$. Prove for all $a \in \mathbb{C}$ except maybe one only complex number $f(z)=a$ has infinite solutions outside any circunference.
The problem also ask for calculating that one complex number in case it exists.
The part of "outside any circunference" gives me a clue of trying to solve it by using the argument principle and the winding number theorem but im struggling to make clear conclussions on what they are helping me on.
I'm glad of receiving your help.