# Imaginary Number

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An Imaginary Number is a Number that is based on a real number multiplied by an imaginary unit.

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**Example(s):**- [math]\displaystyle{ 2 i }[/math].
- [math]\displaystyle{ \pi i }[/math].
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**Counter-Example(s):**- a Real Number.

**See:**Complex Number, Imaginary Unit, Square (Algebra), Real Part, Modular Arithmetic.

## References

### 2014

- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Imaginary_number Retrieved:2014-10-16.
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**imaginary number**is a number that can be written as a real number multiplied by the imaginary unit ,^{[note 1]}which is defined by its property .^{[1]}The square of an imaginary number is . For example, is an imaginary number, and its square is . Except for 0 (which is both real and imaginary^{[2]}), imaginary numbers produce negative real numbers when squared. An imaginary number can be added to a real number to form a complex number of the form , where the real numbers and are called, respectively, the*real part*and the*imaginary part*of the complex number.^{[note 2]}Imaginary numbers can therefore be thought of as complex numbers whose real part is zero. The name "imaginary number" was coined in the 17th century as a derogatory term, as such numbers were regarded by some as fictitious or useless. The term "imaginary number" now means simply a complex number with a real part equal to, that is, a number of the form .

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