If f(z) has a pole of order n at z = a, then residue of function f(z) at a is

Residue Theorem:

If f(z) is analytic in a closed curve C except at a finite number of singular points within C, then

Formula to find residue:

1. If f(z) has a simple pole at z = a, then

2. If f(z) has a pole of order n at z = a, then

Important Points:

Cauchy’s Theorem:

If f(z) is an analytic function and f’(z) is continuous at each point within and on a closed curve C, then

Cauchy’s Integral Formula:

If f(z) is an analytic function within a closed curve and if a is any point within C, then