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GATE ECE 2024 | Question: 33

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​​​​​Let $z$ be a complex variable. If $f(z)=\frac{\sin (\pi z)}{z^{2}(z-2)}$ and $C$ is the circle in the complex plane with $|z|=3$ then $\oint_{C} f(z) d z$ is $\_\_\_\_\_\_$.

  1. $\pi^{2} j$
  2. $j \pi\left(\frac{1}{2}-\pi\right)$
  3. $j \pi\left(\frac{1}{2}+\pi\right)$
  4. $-\pi^{2} j$

 

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