there is a unique mobius transformation taking three points to three points, proof? Watch
distinct points in C, there exists a unique Mobius transformation that
takes zj to wj [j = 1; 2; 3].
Errr, I can't find my notes on this, and I know there's a really snazzy way to do it. Help would be much appreciated.
f(z1) = 0
f(z2) = 1
f(z3) = infinity
w1 = g(0)
w2 = g(1)
w3 = g(infinity)
Wj = gf(Zj)
g and f are bijective, therefore so is gf, and so there exists a unique mobius transformation which takes three distinct points to another three distinct points