# Definition:Complex Number/Imaginary Unit

(Redirected from Definition:Imaginary Unit)

## Definition

Let $\C = \set {a + b i: a, b \in \R}$ be the set of complex numbers.

The entity $i := 0 + 1 i$ is known as the imaginary unit.

## Also denoted as

Using the formal definition of complex numbers it is the ordered pair $\tuple {0, 1}$.

The non-italicized $\mathrm i$ can also be seen.

## Historical Note

The symbol $i$ that is in widespread use for the imaginary unit was due to Leonhard Paul Euler's influence.