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Möbius transformation

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In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form

Möbius transformation - Wikipedia Jump to content From Wikipedia, the free encyclopedia Rational function of the form (az + b)/(cz + d) Not to be confused with Möbius transform or Möbius function . In geometry and complex analysis , a Möbius transformation of the complex plane is a rational function of the form f ( z ) = a z + b c z + d {\displaystyle f(z)={\frac {az+b}{cz+d}}} of one complex variable z ; here the coefficients a , b , c , d are complex numbers satisfying ad − bc ≠ 0 . Geometrically, a Möbius transformation can be obtained by first applying the inverse stereographic projection

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