Exercise · ZW-HOLOMORPHIC-FUNCTION-004 · ★★☆ Intermediate
The function \(f(z)=|z|^2\) is differentiable at \(z=0\). Is it holomorphic on an open set containing \(0\)?
Choose one option.
Show answer
- C. No: it is not differentiable at any nearby point
Explanation
Holomorphic requires differentiability on a whole open set; \(|z|^2\) satisfies Cauchy-Riemann only at the origin.
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 \(U\).
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