Hello,

I am asked, whether for every analytic non-constant function f there exist z such as $\displaystyle \Re f(z) > |f(z)|^2$.

I am pretty sure it is true because I read about Picard's theorems, but I cannot use that. I can use Liouville's Theorem and if needed Cauchy.

I've been trying to assume that for every z, $\displaystyle \Re f(z) \leq |f(z)|^2$ and then find a function g(f(z)) such as the condition bounds g, therefore g is constant and so is f, but with no luck so far.

Thank you!