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GATE Mechanical 2022 Set 2 | Question: 39

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Given $z = x + iy, i = \sqrt{-1}$. $C$ is a circle of radius $2$ with the centre at the origin. If the contour $C$ is traversed anticlockwise, then the value of the integral $\dfrac{1}{2\pi}\int _{C}\dfrac{1}{\left ( z-i \right )\left ( z+4i \right )}dz$ is __________________ (round off to one decimal place).

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