# Complex Numbers

The number *a + bi* is a complex number.

The number** a** is called** the real part** of the** complex number**.

The number** b** is called** the imaginary part** of the** complex number**.

If b = 0, the** complex number** is reduced to a real number as a + 0*i* = a.

If a = 0, the** complex number** is reduced to* bi*, and it is said that it is a

**pure imaginary number**.

The set of all** complex numbers** is denoted by .

The** complex numbers ****a + b i** and

**−a − b**are called

*i***opposites**.

The** complex numbers ****z = a + b i** and

**z**

**= a − b**are called

*i***conjugates**.

Two** complex numbers** are** equal** when they have** the same real component and the same imaginary part. **

## Graphic Representation of Complex Numbers

Complex numbers are represented in the Cartesian axes. The** x-axis **is called** the real axis** and the** y-****axis, imaginary**. **The complex number a + bi ** is represented by:

1 The point **(a, b)**, which is called its **affix**.

Z

2 By a** vector of origin (0, 0) and extreme (a, b). **

The affixes of the real numbers are located on the real axis, X, and the imaginary numbers on the imaginary axis, Y.