Definition:Distance/Points/Complex Numbers

Definition

Let $x, y \in \C$ be complex numbers.

Let $\cmod {x - y}$ be the complex modulus of $x - y$.

Then the function $d: \C^2 \to \R$:

$\map d {x, y} = \cmod {x - y}$

is called the distance between $x$ and $y$.

Also see

• Complex Plane is Metric Space

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Graphical Representation of Complex Numbers
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): distance (in the complex plane)