Question
Evaluate the integral 
where C is the circle IzI = 2.
C∫ez(z2+1)/ (z- 1)2 dz
Answer :
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Skip in 10
Alright, let’s go step-by-step. We want to evaluate \[ I = \int_C \frac{e^z (z^2 + 1)}{(z - 1)^2} \, dz \] where \(C\) is the circle \(|z| = 2\). --- ### 1. Analyze the integrand The integrand is \[ f(z) = \frac{e^z (z^2 + 1)}{(z - 1)^2}. \] We have a pole at \(z = 1\) inside \(C\) since \(|1| = 1 <
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