Question
If $f: D \rightarrow \mathbb{C}$ is analytic, $D \subseteq \mathbb{C}$ is open, and one of the following conditions holds:(a) Re $f=$ constant,(b) $\operatorname{Im} f=$ constant,(c) $|f|=$ constant, then $f$ is locally constant.
Step 1
Step 1: Recall that a function \( f: D \rightarrow \mathbb{C} \) is said to be analytic on an open set \( D \) if it is differentiable at every point in \( D \) and its derivative is continuous. Show more…
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