Definition:Euclidean Metric/Complex Plane

Definition
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 $z_1 - z_2$.

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

Also see

 * Definition:Euclidean Metric on Real Vector Space


 * Complex Plane is Metric Space