Let $f(z)$ be a complex function that is holomorphic on an open subset of the complex plane. Now, if we define another function $g(z)=|f(z)|^2$, can we say anything about the holomorphicity of $g(z)$ for arbitrary $f(z)$? Also, can you give examples where depending on the form of $f(z)$, the function $g(z)$ turns out to be holomorphic or otherwise?
Note: I am not a mathematician, so there may be mistakes in the statement of my problem. Please do point that out.
Note that $g(z)=|f(z)|^2$ is a real valued function.
That is you have a function $u+iv$ for which $v=0$
Cauchy- Riemann theorem could be applied to make a decision regarding the function $g(z)$ being or not being holomorphic.