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
Since is inside
And by the Cauchy Integral formula
Is this right?
But in this following question, I have a problem
As is not inside
How should I go upon this question?