6
$\begingroup$

I need to prove without using Picard's Little Theorem the following statement:

Let $f(z)$ an entire function such that $f(z) \notin \mathbb R$ for every $z \in \mathbb C$. Prove that $f$ is constant.

Do you have a way to do it?

Thanks

  • 2
    Do you know about the maximum principle for the real and imaginary parts of a harmonic function? Or Liouville's theorem and the Cauchy Riemann equations?2011-12-06

1 Answers 1