Definition of Complex Numbers: A complex number is defined to be an ordered pair of real numbers and as . That is, the set of complex numbers is denoted by and is given by

The ordered pair here means the order in which we write and in defining the complex number . For example, the number is not the same as .

In the complex number , the real number is called the real part of and is denoted by or ; the real number is called the imaginary part of and is denoted by or . If the real part of the complex number is zero then the complex number z is called a pure imaginary number . The set of real numbers can be identified as a subset in . Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal.

Geometric Interpretation of Complex Numbers: The complex number can be viewed as a point having Cartesian coordinates in the plane . The -axis and -axis are called the real axis and the imaginary axis respectively. The complex number can also be represented by a vector connecting the