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

2^{2} = 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.

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.

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.

- What are scalars?
- Real numbers
- Integers
- Natural Numbers
- Positive numbers
- Negative numbers
- The uses of negative numbers
- Scientific notation (normal form)
- Complex numbers
- Imaginary numbers

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