Question #140189
Solve by cauchy integral formula
∫Z^2 e^z dz ; C : |z| = 1
1
Expert's answer
2020-10-26T19:54:41-0400

Сauchy integral formula: f(z0)=12πicf(z)(zz0)f(z_0) = \frac{1}{2\pi i}\int_c \frac{f(z)}{(z-z_0)}

cz2ezdz=cz3ezzdzf(z)=z3ez,z0=0\int_c z^2 e^zdz = \int_c \frac{z^3e^z}{z}dz \\ f(z) = z^3 e^z, z_0 = 0

So cz2ez=2πif(z0)=2πi0e0=0\int_cz^2e^z = 2\pi i f(z_0) = 2\pi i *0*e^0 = 0


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