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The value of the integral ∮_C (z+1)/(z²-4) dz in counter clockwise direction around a circle C of radius 1 with center at the point z = -2 is

1. πi/2
2. 2πi
3. -πi/2
4. -2πi

Correct answer: πi/2

Solution

The integral evaluates the residue of the function at the poles inside the contour. The only pole within the circle of radius 1 centered at z = -2 is at z = -1, which contributes a residue of 1/2, leading to the result of πi/2 when multiplied by 2πi.

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