one of my homework problems is the following:
When can a polynomial $p(x,y)$ be expressed as $p(x,y)=f(x+iy)+g(x-iy)$, for $f,g$ holomorphic?
I'm a bit lost after thinking about this question for a long while, as it seems rather vague. I would guess that it would only be possible if the Laurent series of $f(x+iy)$ and $g(x-iy)$ cancel each other out after a certain term, but I don't think this is a very satisfying answer. Would you have any thoughts as to how I might go about this problem? Thanks a bunch in advance.