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# Imaginary-number

An imaginary number is one that when squared gives a negative result.

Normally, with real numbers, when you square them, you always get a positive result.
For example

22 = 4
and
(–3)2 = 9
Recall: A negative times a negative is positive.

With imaginary numbers, when you square them, the answer is negative. They are written like a real number, but with the letter i after them, like this:

23iThe letter i means it is an imaginary number.

## What i really means

The letter i is a number, which when multiplied by itself gives -1. This means that

This makes imaginary numbers very useful when we need to find the square root of a real negative number. For example we normally cannot find the square root of say –16.   But using imaginary numbers we can: We understand this imaginary number result as "4 times the square root of negative one".

Remember: real and imaginary numbers are not "like" quantities. You cannot say, add a real to an imaginary. They are separate types of number.

## They are used in complex numbers

If you pair a real number with an imaginary number, you get a thing called a complex number, which can be plotted on a two-dimensional plane. They look like this: See Complex Numbers for more.