# What are Complex Numbers?

In mathematics, you may find various numbers which are mostly classified on the basis of factors. One such number is a complex number, a number that can be defined as the value obtained by the addition of a real number with an imaginary number. It is written as a + ib where b and a are considered as real numbers and i is denoted as the imaginary number. Real numbers are those numbers that include all numbers except __complex numbers__.

Some examples of real numbers are rational and irrational numbers, integers, whole numbers, natural or counting numbers, and so on. The complex numbers are usually represented with the help of the letter ‘z’. This term was coined by the Greek mathematicians for the hero of Alexander. Later on, it is believed that these numbers were originated by a bunch of mathematicians which included Gerolamo Cardano. The complex numbers have a range of applications such as fluid dynamics, the concept of quantum mechanics, vibration analysis, and many more. We shall cover some interesting topics related to complex numbers such as properties of this number, comparison between complex and real numbers, and many more.

## Some Important Properties of Complex Number

The following are the significant properties of a complex number :

- A complex number is produced when the arithmetic operation of addition takes place between an imaginary and complex number.
- Conjugate complex numbers are a type of complex number. When the addition of conjugate complex numbers takes place, a real number is formed.
- A complex number will always obey the additive property of multiplication and addition.
- Have you ever observed the multiplication of two binomials? This process is similar to the multiplication of two complex numbers.

Using these points, you will be able to differentiate between various numbers.

## Complex Numbers Vs Real Numbers

The following points mentioned below signifies some important points which differentiate a complex number from a real number:

- A real number is a type of number which includes all types of numbers except the number which is complex whereas a complex number is a number that can be defined as the value obtained by the addition of a real number with an imaginary number.
- A real number can be placed or plotted in a graph whereas a complex number can never be plotted on a graph.
- The symbol which is used to denote a real number is R. The symbol which is used to denote a complex number is Z.
- Some Examples of the real numbers are as follows: 2, 3, 4, 5, and so on. Some examples of complex numbers are as follows: 5 + 2i , 3 + 2i, and many more.

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