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

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.

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 $C$