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

QB_PH_023: Complex analysis

Question Statement

What is the order of the pole of $f(z) = \frac{1}{z^3 \sin(z)}$ at $z = 0$?
Correct Answer
4, 4
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: $\sin(z) = z(1 - z^2/6 + \dots)$, so $z^3 \sin(z) = z^4(1 - \dots)$. Pole order is 4.
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