möbius transformations

Möbius transformations are a type of complex function that map the extended complex plane onto itself in a bijective manner. They are defined by the formula T(z) = (az + b) / (cz + d), where a, b, c, and d are complex numbers with ad - bc ≠ 0. These transformations preserve angles, circles, and lines in the complex plane and can be used to perform operations such as rotations, translations, dilations, and inversions.

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