Complex numbers are used extensively in DSP because they make explaining things far easier.

You should already be away of certain mathematical sets of numbers like the Integers, the Rationals and the Reals. You should also be aware that the Rationals is a superset of the Integers and the Reals is a superset of the Integers

The set of Complex numbers is a superset of the Reals, and each Complex number can be expressed as :

where both a and b are numbers in the set of Reals and j is a mathematical constant such that:

In order the remain consistent with the rest of mathematics ,