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

1. 4πi
2. 0
3. 2πi
4. 2π - 2i

Correct answer: 0

Solution

The integrand simplifies to 1 everywhere except at the poles, which are at z = ±2. Since both poles lie outside the contour defined by |z - i| = 2, the integral evaluates to zero due to the absence of singularities within the contour.

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