Q: Evaluate the following integral using residue theorem
∫z^2 e^z dz ; C : |z| = 1
1
Expert's answer
2020-10-28T18:30:03-0400
Consider the integral ∫Cz2ez where C={z∈C:∣z∣=1}. The function f(z)=z2ez has no a singular point, and is a holomorphic function in D={z∈C:∣z∣≤1}. Therefore, Cauchy’s residue theorem implies ∫Cz2ez=0.
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