Mobius transformations
General · Mathematics
Study notes
Q: Find the Möbius map sending 0→1, 1→∞, ∞→0. What is it? 0→1: b/d = 1: b = d. 1→∞: c+d = 0: c = -d. ∞→0: a/c = 0: a = 0. w = (0·z+d)/(-dz+d) = d/(d(1-z)) = 1/(1-z). Check: w(0) = 1 ✓, w(1) = ∞ ✓, w(∞) = 0 ✓! (Involution? w(w(z)) = z: yes!)