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The residue of the function f(z) = 1 / ((z + 2)² (z - 2)²) at z = 2 is

1. (A) -1/32
2. (B) -1/16
3. (C) 1/16
4. (D) 1/32

Correct answer: (A) -1/32

Solution

At the double pole z=2, residue = d/dz[(z-2)^2 f(z)] = d/dz[1/(z+2)^2] = -2/(z+2)^3. Evaluated at z=2: -2/(4)^3 = -2/64 = -1/32.

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