An entire function whose imaginary part is bounded is constant – math.stackexchange.com

An entire function whose imaginary part is bounded is constant – math.stackexchange.com

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I need to prove the following question Question Let $g(z)$ be an entire function such that there exists an $\alpha > 0$ such that $\left|\operatorname{Im}(g(z))\right| \le \alpha$. Prove that ...

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