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 + 0i = 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 + bi and −a − bi are called opposites.
The complex numbers z = a + bi and z = a − bi are called 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.
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.