Looks like a Mobius transformation which is rational function f : C -> C, on the complex plane, of the form f(z) = (a z + b) / (c z + d). The key feature is t

Looks like a Mobius transformation which is rational function f : C -> C, on the complex plane, of the form f(z) = (a z + b) / (c z + d). The key feature is that this is a conformal transformation which means it preserves angles (between curves). Reading it a bit more I guess thats clear.