Answer to Question #140189 in Complex Analysis for Usman

Question

Solve by cauchy integral formula
∫Z^2 e^z dz ; C : |z| = 1

Answer 1

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

$\int_c z^2 e^zdz = \int_c \frac{z^3e^z}{z}dz \\ f(z) = z^3 e^z, z_0 = 0$

So $\int_cz^2e^z = 2\pi i f(z_0) = 2\pi i *0*e^0 = 0$