Imaginary numbers allow us to represent the square root of a negative number or the product of a real number and the imaginary unit, j. The square root of a negative number is called a pure imaginary number. The symbol represents the principal square root of a and is never negative. If a is a real number, then is a pure imaginary number and where

Example 1

Note: since






Rectangular form of a complex number

The form a+bj is known as the rectangular form of a complex number, where a is the real part and b is the imaginary part.

Two complex numbers are equal if both the real parts are equal and the imaginary parts are equal.

Given a+bj and c+dj are two complex numbers. Then, a+bj = c+dj if and only if a=c and b=d.

Example 2 Solve 4+3j = (x+2) + 7j + yj

Real parts are equal
4=x+2
2=x

Imaginary parts are equal
3j=7j+yj
3=7+y
-4=y