Möbius Transformations Invariance of the Cross Ratio 1

Proof of the invariance of the cross ratio under Möbius transformations. 3 cases are considered: 1) When z1, z2, z3, z4, f(z1), f(z2), f(z3), f(z4) are all finite, 2) When z1, z2, z3, z4, f(z1), f(z2), f(z3) are all finite but f(z4) = point at infinity, and 3) z1, z2, z3, f(z1), f(z2), f(z3), f(z4) are all finite but z4 = point at infinity.
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