Exercise · ZW-HOLOMORPHIC-FUNCTION-002 · ★☆☆ Basic
On which set is \(f(z)=1/z\) holomorphic?
Choose one option.
Show answer
- D. \(\mathbb{C}\setminus\{0\}\)
Explanation
The difference quotient exists at every \(z\neq0\), with \(f'(z)=-1/z^2\); at \(0\) the function is not even defined.
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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