The problem we've been given is the following a) The integral of f(z) = 1/[(z-5)(z-8)] around the circle of radius one centered at z=1 with positive orientation has value zero. (T/F)
b)Let C be the circle of radius fifty centered at the origin with positive orientation.
If F(z)=[1/(z-i)] + [1/(z-2)] then the integral around C of F(z) has value:
The first one should be 0 because none of the points at which the function is not analytic are in the bounds. About the second one, I'm not sure how to proceed? Since both things are in the bound it's multiply connected. Can we use the deformation of contours to get the value of both the integrals as 2(pi)i and thus the final computation as 4(pi)i.