, C is along the circle |z|=1

and

another case, C along the circle |z-1|=1.

. C is |z|=1, and |z-1|=1

i think the first part is the same for both cases which is 2pi*i.

and the second part is 0 for both cases by Cauchy Integral Theorem.

But i am not sure if that can be applied. Because sqrt z is only analytic on C\ { x axis } . Therefore, out circles are not connected?