Answer to Question #140920 in Complex Analysis for Usman

Question #140920

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\int_C z^2e^z where C={zC:z=1}C=\{z\in\mathbb C: |z|=1\}. The function f(z)=z2ezf(z)=z^2e^z has no a singular point, and is a holomorphic function in D={zC:z1}D=\{z\in\mathbb C: |z|\leq 1\}. Therefore, Cauchy’s residue theorem implies Cz2ez=0.\int_C z^2e^z =0.


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