# Complex Analysis : Complex Integration

## Example Questions

### Example Question #1 : Complex Integration

Let  be the region of the complex plane enclosed by

Compute

Explanation:

Recall Cauchy's integral formula, which states

In this case, we have

Plugging in gives us

### Example Question #1 : Complex Integration

Let be the unit circle.

Compute

Explanation:

Recall the Taylor expansion of

Use this to write

The coefficient of  is the residue, so by the residue theorem, the value of the integral is