### Imaginary number

An **imaginary number** has no real value. You write it as

i y

where *i* is the imaginary unit.

##### Explanation

Imaginary numbers are part of a complex number, that is denoted by the letter *z *as

z = x + iy

where *x* and *y* are real numbers, and *i* de imaginary unit. A complex number has a real part and an imaginary part. You can say that *iy* is an imaginary number, but it is also a complex number, because

z= 0 +iy

And *i* itself is also a complex number, because

i= 0 + 1i

it consists only of an imaginary part. It has no real value. Every real number is a complex number, because

x = x+ 0i

The name 'imaginary number' is not widely used in practice. Sometimes you find 'imaginary pure' instead. It always describes the imaginary part of a complex number. They can be found in exponential functions and then the distinction is not important. There you get

where each term can be handled separately.