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.