Exercise · ZW-HOLOMORPHIC-FUNCTION-003 · ★☆☆ Basic
Saying that \(f\) is holomorphic on an open set \(U\) means that:
Choose one option.
Show answer
- A. it is complex differentiable at every point of \(U\)
Explanation
Holomorphy requires a complex derivative at every point of the open set, not merely continuity or partial derivatives.
Review the concept: Holomorphic function
A complex function \(f\) is holomorphic on an open set \(U\) of the plane if it is complex differentiable at every point of \(U\).
More practice problems: holomorphic function
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- ZW-HOLOMORPHIC-FUNCTION-009 If f is holomorphic on a connected open set U and u=Ref is constant, what follows?