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Möbius transformations are conformal, bilinear functions of the form
:<math>t = f(z) = \frac{az + b}{cz + d},</math>
where <math>t, z \in \widehat{\mathbb{C}}</math>, <math>a, b, c, d \in \mathbb{C}</math>, and <math>ad - bc \neq 0</math>. It is an automorphism of the Riemann sphere, and the set of all Möbius transformations on the Riemann sphere forms the automorphism group.
:<math>t = f(z) = \frac{az + b}{cz + d},</math>
where <math>t, z \in \widehat{\mathbb{C}}</math>, <math>a, b, c, d \in \mathbb{C}</math>, and <math>ad - bc \neq 0</math>. It is an automorphism of the Riemann sphere, and the set of all Möbius transformations on the Riemann sphere forms the automorphism group.