Definition:Complex Number/Imaginary Unit

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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.