Question Bank MCQ • 2 Marks Section 1: Mathematical Physics Complex analysis

QB_PH_005: Complex analysis

Question Statement

The residue of $f(z) = \frac{z^2}{(z - 1)^2 (z + 2)}$ at the second-order pole $z = 1$ is:
(A) \frac{5}{9}
(B) \frac{4}{9}
(C) \frac{1}{3}
(D) \frac{2}{9}
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: Calculate $\lim_{z \to 1} \frac{d}{dz}\left[\frac{z^2}{z + 2}\right] = \frac{2(1)(3) - 1^2}{(3)^2} = \frac{5}{9}$.
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