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Integration of the complex function f(z) = z²/(z² - 1), in the counterclockwise direction, around |z| = 1, is

1. -πi
2. 0
3. πi
4. 2πi

Correct answer: 0

Solution

The function f(z) = z²/(z² - 1) has poles at z = 1 and z = -1, which lie outside the contour |z| = 1. Since there are no singularities within the contour, the integral evaluates to zero by the residue theorem.

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