Question

Integral cosz dz/(z (z-2) (z-4)) at |z|=1

Answer 1

\[\Large \oint\limits_\gamma^{}\frac{\cos(z)}{z(z-1)(z-4)}dz\qquad \gamma = \{z \ \ | \ \ |z|=1\}\]

Answer 2

Looks daunting? :D

Answer 3

@rrakes
Stay with me ^_^

Answer 4

i need solution and the concept to solve.

Answer 5

Gladly. First, Cauchy-Goursat theorem.
This integrand is analytic everywhere except for a few points known as poles.
Can you identify the poles?

Answer 6

yes 0 2 4

Answer 7

2?
I don't think so :)

Answer 8

z-2 is there in denominator and at z=2 the integrand is not defined

Answer 9

There is no z-2 in your post -_-
No matter:
Is this the correct integral:
\[\Large \oint\limits_\gamma^{}\frac{\cos(z)}{z(z-2)(z-4)}dz\]

Answer 10

@rrakes
This is kind of important ^_^

Answer 11

yes