Let \(f\) be an entire function such that \(|\Re f(z)|+|\Im f(z)|\ge 1\) for each \(z\in \mathbb C\). Prove that \(f\) is a constant function.
Question
Math 6210 • Real Analysis
2004 • Question 7
Question
2004 • Question 7
Let \(f\) be an entire function such that \(|\Re f(z)|+|\Im f(z)|\ge 1\) for each \(z\in \mathbb C\). Prove that \(f\) is a constant function.