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

Bear in mind that Euclid himself did not in fact conceive of the Euclidean metric. It is called that because the geometric space which it gives rise to is Euclidean in the sense that it is consistent with Euclid's fifth postulate.