Definition:Complex Number/Definition 1

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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 complex numbers is usually denoted $\C$.

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 $3 + 4 i$.

Also see

  • Results about complex numbers can be found here.