\begin{definition}[Definition:Distance/Points/Complex Numbers]
Let $x, y \in \C$ be complex numbers.
Let $\cmod {x - y}$ be the complex modulus of $x - y$.
Then the function $d: \C^2 \to \R$:
:$\map d {x, y} = \cmod {x - y}$
is called the '''distance between $x$ and $y$'''.
\end{definition}