Definition:Complex Number

Formal Definition
The set of all complex numbers is denoted $\C$.

Also denoted as
Variants on $\C$ are often seen, for example $\mathbf C$, $\CC$ and $\mathfrak C$, or even just $C$.

When $a$ and $b$ are symbols representing variables or constants, the form $a + i b$ is usually (but not universally) seen.

Similarly, when $a$ and $b$ are actual numbers, for example $3$ and $4$, it is usually (but not universally) written $3 + 4 i$.

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

 * Equivalence of Definitions of Complex Number

The $a + i b$ notation usually proves more convenient; the ordered pair version is generally used only for the formal definition as given above.


 * Definition:Complex Addition
 * Definition:Complex Multiplication