Let A, for i = 1,2,3, 4 be four distinct points in the complex plane and let Bi for i = 1,2, 3, 4 be as well four distinct points. Show that there exists a Mobius transformation sending A, to B, for i = 1,2,3, 4 if and only if the cross ratios satisfy (A1, A2, A3, A4) = (B1, B2, Ba, B4). %3D (Recall that the cross ratio is defined by (A, B, C, D) = 4-.B-D.)
Let A, for i = 1,2,3, 4 be four distinct points in the complex plane and let Bi for i = 1,2, 3, 4 be as well four distinct points. Show that there exists a Mobius transformation sending A, to B, for i = 1,2,3, 4 if and only if the cross ratios satisfy (A1, A2, A3, A4) = (B1, B2, Ba, B4). %3D (Recall that the cross ratio is defined by (A, B, C, D) = 4-.B-D.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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