Linear fractional transformation

A linear fractional transformation (LFT), also known as a Möbius transformation, is a function that maps the complex plane to itself. It is defined by the formula: \[ f(z) = \frac{az + b}{cz + d} \] where \(a\), \(b\), \(c\), and \(d\) are complex numbers, and \(ad - bc \neq 0\) to ensure that the transformation is well-defined and non-degenerate.