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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. 2πi
4. 2π

Correct answer: 0

Solution

The integral evaluates to zero because the integrand has no poles inside the contour |z| = 2. The poles at z = 2i and z = -2i are outside this contour, leading to a result of zero by the residue theorem.

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