Imaginary numbers – What it is, definition and concept

Imaginary numbers are part of the set of complex numbers and are the product of a real number and the imaginary unit i.

In other words, imaginary numbers are complex numbers and can be written as the multiplication of the imaginary unit i by any real number.

The i to denote the imaginary unit since it comes from English, imaginary numbers.

Imaginary number formula

Given an imaginary number r, it can be expressed as:

r = n i


  • r it is an imaginary number.
  • n is a real number.
  • i is the imaginary unit.


Complex Numbers Scheme 1
Position of imaginary numbers within complex numbers

Imaginary numbers example

In the mathematical operations that we do every day we find imaginary numbers more times than we think. Let’s see it by solving the following square root:

Example Imaginary Numbers
Example of an imaginary number

How many times have we been solving a quadratic equation and said there was no solution because we found a negative root? Well, this negative rootWhatever it is, it can be decomposed, as indicated above, and have a real number and the imaginary unit. In this case, the real part is the number 8 and the imaginary part is the square root of -1.

The square root of -1 is known as the imaginary unit.

Imaginary Unit
Imaginary unit

So the solution of this root would be:

Solution of a Negative Square Root
Solution of a negative square root

Recalling the previous definition, we know that a imaginary number is equal to the multiplication of one real number anyone for the imaginary unit. Then:

Solution Of A Negative Square Root 1
Solution of a negative square root

Imaginary numbers are part of the set of complex numbers which is divided between real numbers and imaginary numbers.


It seems that the idea of ​​imagining numbers is not very convincing, but they really are very useful. Given the previous example, imaginary numbers give answers to problems that real numbers cannot.

Now when we find a negative root we can solve the problem.


Imaginary numbers are widely used in the field of electricity, in quantum mechanics, in Fourier transformations and, combined with real numbers, create complex numbers, also widely used in the field of mathematics.


Imaginary numbers were named imaginary for mockery since they were conceived as an impossible numerical set and contrary to real numbers.

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