GATE 2019 EC – Question 26
The value of the contour integral
$$\frac{1}{2\pi j}\oint\left(z+\frac1z\right)^2dz$$
evaluated over the unit circle $|z|=1$ is ________.
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Show answer and explanation
Correct answer: 0
Explanation
$\left(z+\frac1z\right)^2=z^2+2+z^{-2}$. The integral picks out the coefficient of $z^{-1}$, which is 0, so the value is 0.