f(z) analytic, 1/2πi inte. f’(z) /f(z) dz=N-P, N zero and P poles inside C. (CA -I-50.H R BHAGAT.)

If f(z) is analytic within and on a closed contour C excoept at a finite number of poles and is not zero on C, then
1/2πi integeral over C f'(z) /f(z) dz equal to N minus P,
where N is the number of zeros and P is the number of poles inside C.
CA-I-50.
HUKAM RAJ BHAGAT.