Is $|z^2|$ entire function?

Question

I want to know whether $|z^2|$ is entire function or not.

If I am not wrong then $z^2$ is entire but $|z|$ is not entire (Am I wrong here?)

So, now how to say anything whether $|z^2|$ is entire or not?

Answer 1

A real valued function cannot be entire (unless is constant), as you can quickly see checking the Cauchy-Riemann equations