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The value of the contour integral ∮_C ((z+2)/(z²+2z+2)) dz, where the contour C is {z: |z + 1 - 3j/2| = 1}, taken in the counter clockwise direction, is

1. -π(1 + j)
2. π(1 + j)
3. π(1 - j)
4. -π(1 - j)

Correct answer: π(1 + j)

Solution

The integral evaluates to π(1 + j) because the integrand has a pole inside the contour defined by C, and by applying the residue theorem, we find that the residue at the pole contributes this value to the integral.

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