Let \(f\) be an entire function such that for each \(z\in \mathbb C\), \[ \operatorname {Re} f(z)\cdot \operatorname {Im} f(z)\ne 1. \] Prove that \(f\) is a constant.
Question
Math 6210 • Real Analysis
Fall 2017 • Question 7
Question
Fall 2017 • Question 7
Let \(f\) be an entire function such that for each \(z\in \mathbb C\), \[ \operatorname {Re} f(z)\cdot \operatorname {Im} f(z)\ne 1. \] Prove that \(f\) is a constant.