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The value of the integral ∮_c (-3z + 4)/(z² + 4z + 5) dz where c is the circle |z| = 1 is given by

1. 0
2. 1/10
3. 4/5
4. 1

Correct answer: 0

Solution

The integral evaluates to zero because the integrand is analytic inside the contour defined by |z| = 1, and by Cauchy's integral theorem, the integral of an analytic function over a closed curve is zero.

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