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

1. 4πi
2. 0
3. 2πi
4. 2 - 2i

Correct answer: 0

Solution

The integrand simplifies to 1 for all points except where the denominator is zero, which occurs at z = ±2. Since the contour |z| = 2 does not enclose any singularities, the integral evaluates to zero by the residue theorem.

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