\begin{definition}[Definition:Complex Number/Definition 1]
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 $\C$.
\end{definition}