Isometric Metric Spaces/Examples
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Examples of Isometric Metric Spaces
Euclidean Plane is Isometric to Complex Plane
Let $\R^2$ be the real number plane with the Euclidean metric.
Let $\C$ denote the complex plane.
Let $f: \R^2 \to \C$ be the function defined as:
- $\forall \tuple {x_1, x_2} \in \R^2: \map f {x_1, x_2} = x_1 + i x_2$
Then $f$ is an isometry from $\R^2$ to $\C$.