If z1, z2, z3, z4 are complex number
s, then the quantity:
------- * -------
is called the cross ratio
of the 4-tuple
The cross ratio is conserved
(a*z). For such a transformation
s, the cross ratio of (s(z1),s(z2),s(z3),s(z4)).
In the complex numbers, any transformation s that is a composition of these four simple transformations is of the form:
a*z + b
s(z) = -------
c*z + d
where a,b,c,d,z are complex numbers.
From this it is simple calculation to verify that the cross ratio is conserved.