Exercise · ZW-COMPLEX-DERIVATIVE-001 · ★☆☆ Basic
Compute \(f'(3)\) for \(f(z)=z^2\).
Choose one option.
Show answer
- A. \(6\)
Explanation
The quotient is \(\frac{(3+h)^2-9}{h}=6+h\), which tends to \(6\) as \(h\to0\).
Review the concept: Complex derivative
The derivative \(f'(z_0)\) of a complex function \(f\) at a point \(z_0\) is the limit of the difference quotient as \(z\) approaches \(z_0\) from any direction in the plane, if that limit exists.
\[f'(z_0)=\lim_{z\to z_0}\frac{f(z)-f(z_0)}{z-z_0}\]
More practice problems: complex derivative
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- ZW-COMPLEX-DERIVATIVE-008 Compute h'(1) for h(z)=(z^2)/(z+1).
- ZW-COMPLEX-DERIVATIVE-009 For f(z)=bar z at z_0=2, what happens to the difference quotient?