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Given f(z) = 1/(z+1) - z²/(z+3). If C is a counterclockwise path in the z-plane such that |z+1|=1, the value of (1/(2πi)) ∮_C f(z) dz is

1. -2
2. -1
3. 1
4. 2

Correct answer: 1

Solution

The contour |z+1|=1 encloses only z=-1. The residue of 1/(z+1) there is 1, and the term z^2/(z+3) has its pole at z=-3 outside the contour. So (1/(2*pi*i))*integral = 1, not -1.

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