## 16

## Complex Integration

##### 16.0 INTRODUCTION

Integrals are extremely important in the study of functions of a complex variable mainly for two reasons. Some properties of analytic functions can be proved by complex integration easily. For instance, the existence of higher derivatives of analytic functions. Secondly in applications real integrals occur which cannot be evaluated by usual methods, but can be evaluated by complex integration.

We know that definite integral of a real function is defined on an interval of the real line. But integral of a complex valued function of a complex variable is defined on a curve or arc in the complex plane. A complex definite integral is called a (complex) line integral.

#### Definition 16.1 Contour

A **contour** is a ...