# What are imaginary numbers?

##### 1 Answer

#### Answer:

The Real numbers can be represented as a line.

The Complex numbers can be represented by a plane whose

Imaginary numbers are the numbers on the

#### Explanation:

Suppose we start with Whole numbers

We can add them them quite happily and we always get another Whole number.

We can solve problems like

So we can introduce the idea of a negative number and expand our idea of what a number is to include all of the Integers:

#ZZ = { 0, 1, -1, 2, -2, 3, -3,...}#

We can add and multiply any two Integers and we always get an Integer.

We can solve problems like

So we can introduce the idea of a Rational number and expand our idea of what a number is to include all numbers of the form

...

To cut a long story short, in order to be able to solve problems like

A square root of a negative Real number is a pure imaginary number.

In fact, we define the principal square root of a negative Real number as:

#sqrt(x) = i sqrt(-x)#

Any Complex number

Please note that Imaginary numbers are no more imaginary than Real numbers. Sir Isaac Newton seemed to dislike working with negative numbers, which he called "imaginary" numbers.