The solution to 1) is correct. For the second problem, the function z/(z–2) is analytic everywhere inside the circle |z|=1, so by Cauchy's theorem the integral is 0.
Evaluate the following closed contour integral
1)
with
Since is inside
Let
And by the Cauchy Integral formula
So
Thus
Is this right?
But in this following question, I have a problem
with
As is not inside
How should I go upon this question?