and define the cross ratio of complex numbers: the cross ratio of any four distinct finite points 
, 
, 
and 
in that order isI begin with a review of complex numbers and their properties (essential since all the calculations and proofs of the course are based on complex numbers, and the students are usually weak in this area).
I then introduce the "special" number and define the cross ratio of complex numbers: the cross ratio of any four distinct finite points , , and in that order is
or, if is ,
.
Cross ratios have several symmetry properties which ensure that if the cross ratio of four points is known, so is the cross ratio of any permutation of these points.