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.
22 = 4
(–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.
Other number topics
Numbers that have factors
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