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∫ (z² − 4)/(z² + 4) dz evaluated anticlockwise around the circle |z| = 2, where i = √−1, is

1. 4π
2. 0
3. 2π
4. 2πi

Correct answer: 0

Solution

The integral evaluates to zero because the integrand has no poles inside the contour |z| = 2, as the only singularities occur at z = ±2i, which lie outside the circle. By the residue theorem, since there are no residues to account for within the contour, the integral results in zero.

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