I have been asked the following question and would appreciate an explanation.
Suppose we have to find an analytic function $F(z)$ where $z=x+iy\in \mathbb C$ and its real part is $g(x,y)$. Question: Does it suffice to be given $F(z)=g(z,0)$ for us to determine $F(z)$ in general?
I am not sure though I guess the fact that analytic functions only depend on $z$ might be relevant? (I might be wrong though!)
Thank you.