Exercise · ZW-HOLOMORPHIC-FUNCTION-007 · ★★☆ Intermediate
Let \(f=u+iv\) with \(u=x^2-y^2\) and \(v=axy\). For which value of \(a\) is \(f\) holomorphic?
Choose one option.
Show answer
- B. \(a=2\)
Explanation
\(u_x=2x\) and \(v_y=ax\) force \(a=2\); the other equation, \(u_y=-2y=-v_x=-ay\), gives the same.
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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