mobius transformation

A Möbius transformation is a relation between complex numbers defined by the formula \( f(z) = \frac{az + b}{cz + d} \), where a, b, c, and d are complex numbers with ad - bc ≠ 0. It is a type of linear fractional transformation that maps the complex plane onto itself in a bijective and conformal manner. This transformation preserves angles and the orientation of curves, making it a fundamental concept in complex analysis and geometry.

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