Suppose f(z) is a meromorphic function (i.e., f (z) is analytic everywhere in the finite z plane except at isolated points where it has poles) with N simple zeroes (i.e., f(20) = 0, f'(zo) ≠ 0) and M simple poles inside a circle C. Show
1/2πi ∮c f'(z)/f(z) dz = N - M