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C is a closed path in the z-plane given by |z| = 3. The value of the integral ∮_C ((z² − z + 4j)/(z + 2j)) dz is

1. −4π(1 + j2)
2. 4π(3 − j2)
3. −4π(3 + j2)
4. 4π(1 − j2)

Correct answer: 4π(1 − j2)

Solution

The integral evaluates to 4π(1 − j2) because the integrand has a simple pole at z = -2j, which lies within the contour |z| = 3. By applying the residue theorem, we find the residue at this pole and multiply it by 2πi, leading to the final result.

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