Definition:Euclidean Metric/Complex Plane

Definition
Let $\C$ be the complex plane.

The Euclidean metric on $\C$ is defined as:
 * $\displaystyle \forall z_1, z_2 \in \C: d \left({z_1, z_2}\right) := \left\vert{z_1 - z_2}\right\vert$

where $\left\vert{z_1 - z_2}\right\vert$ denotes the modulus of $z_1 - z_2$.

Also known as
The Euclidean metric is sometimes also referred to as the usual metric.

Also see

 * Definition:Euclidean Metric/Real Vector Space


 * Complex Plane is Metric Space