How we solve those?
For the first one, if , then we can use Cauchy's Theorem to change the curve to a point through a homotopy and the integral over a point is zero.
For n=-1 use Cauchy's Integral formula to conclude the answer is
For then we have to use Cauchy's General Integral Formula which is where is the n-th derivative of f(z) evaluated at the point a
for k=-n and by Cauchy's Integral formula this integral is
but f(z)=1 in this case, so the k-1 derivative of 1 is 0 (as k-1 is always at least 1) and anything times 0 is 0.