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geft
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Homework Statement
Integrate (z^2 - 4)/(z^2 + 4) counterclockwise around the circle |z - i| = 2.
Homework Equations
Cauchy's integral formula
The Attempt at a Solution
|z - i| = 2
|z - 2| = i
z0 = 2
(z^2 - 4)/(z^2 + 4)
= ((z + 2)(z - 2))/(z^2 + 4)
= (z + 2)/(z^2 + 4) * i
f(z) = (z + 2)/(z^2 + 4)
2i*pi*f(z0) = 2i*pi*(1/2) = i*pi
The answer is -4*pi. Please tell me what I'm doing wrong.