Definition:Cross-Ratio/Complex Analysis

Theorem
Let $z_1, z_2, z_3, z_4$ be distinct complex numbers.

The cross-ratio of $z_1, z_2, z_3, z_4$ is defined and denoted:
 * $\paren {z_1, z_3; z_2, z_4} = \dfrac {\paren {z_1 - z_2} \paren {z_3 - z_4} } {\paren {z_1 - z_4} \paren {z_3 - z_2} }$

Also known as
Some sources do not hyphenate: cross ratio.

Also see

 * Möbius Transformation Preserves Cross Ratio