Theorem 10.3 (The Implicit Formula). There exists a unique bilinear transformation that maps three distinct points [Graphics:Images/MobiusTranformationMod_gr_93.gif]  onto three distinct points [Graphics:Images/MobiusTranformationMod_gr_94.gif], respectively.  An implicit formula for the mapping is given by the equation    

(10-18)            [Graphics:Images/MobiusTranformationMod_gr_95.gif].  

Proof.

Proof of Theorem 10.3 is in the book.

 

Complex Analysis for Mathematics and Engineering