Question Bank MCQ • 1 Mark Section 1: Mathematical Physics Complex analysis

QB_PH_015: Complex analysis

Question Statement

The value of the contour integral $\oint_{|z|=3} \frac{e^{2z}}{(z + 1)^3} dz$ traversed counter-clockwise is:
(A) 4\pi i e^{-2}
(B) 2\pi i e^{-2}
(C) \pi i e^{-2}
(D) 8\pi i e^{-2}
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: $\oint \frac{f(z)}{(z - z_0)^3} dz = \frac{2\pi i}{2!} f''(z_0)$. With $f(z) = e^{2z}$, $f''(z) = 4e^{2z}$. At $z = -1$: $\pi i (4e^{-2}) = 4\pi i e^{-2}$.
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