Answer to Question #91400 in Complex Analysis for Sajid

Question

Q.Choose the correct answer.
Q. Let C=|z-2|=5, then evaluate the complex integral ∫_C▒〖(z^4 〗+4z)〖cos〗^2 zdz
a. 1
b. 0
c. π
d. -1

Answer 1

Integrand is analytic in region $|z-2|<5$ because it can be represented as a convergent power series in any point of the region. So according to Cauchy's integral theorem the integral is equal to 0. Answer: b.0