\begin{definition}[Definition:Euclidean Metric/Complex Plane]
Let $\C$ be the complex plane.
The '''Euclidean metric''' on $\C$ is defined as:
:$\d \forall z_1, z_2 \in \C: \map d {z_1, z_2} := \size {z_1 - z_2}$
where $\size {z_1 - z_2}$ denotes the modulus of $z_1 - z_2$.
\end{definition}