Definition:Complex Number/Imaginary Unit

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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.