Definition:Complex Number/Definition 1

Definition
A complex number is a number in the form $a + b i$ or $a + i b$ where:
 * $a$ and $b$ are real numbers
 * $i$ is a square root of $-1$, that is, $i = \sqrt {-1}$.

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

Also see

 * Equivalence of Definitions of Complex Number