Let $f : \mathbb{C} \longrightarrow \mathbb{C}$ be an entire function. Suppose that $f(z) \in \mathbb{R}$ if $z$ is on the real axis or on the imaginary axis. Show that $f'(z) = 0$ at $z = 0$.
Let $f : \mathbb{C} \longrightarrow \mathbb{C}$ be an entire function. Suppose that $f(z) \in \mathbb{R}$ if $z$ is on the real axis or on the imaginary axis. Show that $f'(z) = 0$ at $z = 0$.