# Definition:Complex Number/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

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

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

When mathematics is applied to engineering, in particular electrical and electronic engineering, the symbol $j$ is usually used

This is because $i$ is the standard symbol used to denote the flow of electric current, and to use it also for $\sqrt {-1}$ would cause untold confusion.

In some mathematical traditions, the Greek symbol $\iota$ (iota) is used for $i$.

## Also see

- Results about
**the imaginary unit**can be found**here**.

## Historical Note

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

## Sources

- 1960: Walter Ledermann:
*Complex Numbers*... (previous) ... (next): $\S 1.1$. Number Systems - 1968: Murray R. Spiegel:
*Mathematical Handbook of Formulas and Tables*... (previous) ... (next): $6$: Complex Numbers - 1981: Murray R. Spiegel:
*Theory and Problems of Complex Variables*(SI ed.) ... (previous) ... (next): $1$: Complex Numbers: The Complex Number System - 1998: Yoav Peleg, Reuven Pnini and Elyahu Zaarur:
*Quantum Mechanics*... (previous) ... (next): Chapter $2$: Mathematical Background: $2.1$ The Complex Field $C$