GATE 2021 IN – Question 34
For $f(z)=1/(z^2+6z+9)$ in the complex plane, $\oint_C f(z)\,dz$ around the circle centred at the origin with unit radius is ______.
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Show answer and explanation
Correct answer: 0 to 0
Explanation
The denominator z²+6z+9=(z+3)² has its only pole at z=−3, outside |z|=1. The function is analytic on and inside the contour, so Cauchy’s integral theorem gives **0**. There is no enclosed residue.