Answer to Question #13343 in Complex Analysis for Han

Question

Find integral: int(dz/z) on curve C={z=x+iy| abs(z-2)=1 oriented clockwise}

Answer 1

function 1/z has a pole at the point z=0. So If our curve does not contain this point. the integral equals to zero. our circle |z-2|=1 is centered at point 2, with radius 1, So point z=0 is outside our curve.
So, int (dz/z) = 0.