Finding Fixed Points of a Mobius transformation

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SUMMARY

The discussion focuses on finding fixed points of the Mobius transformation defined by the equation m(z) = (2z + 5)/(3z - 1). Participants agree that fixed points are values of z that satisfy the equation m(z) = z. This leads to solving the equation (2z + 5)/(3z - 1) = z, which simplifies to a quadratic equation. The solution involves identifying the roots of this quadratic to determine the fixed points.

PREREQUISITES
  • Understanding of Mobius transformations
  • Familiarity with solving quadratic equations
  • Knowledge of complex numbers
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the properties of Mobius transformations
  • Learn how to derive fixed points from complex functions
  • Explore quadratic equations and their roots in depth
  • Investigate applications of Mobius transformations in complex analysis
USEFUL FOR

Students studying complex analysis, mathematicians interested in transformations, and anyone looking to deepen their understanding of fixed points in mathematical functions.

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Homework Statement



Find all the fixed points to the following Mobius transformation.

Homework Equations



m(z) = (2z + 5)/(3z - 1)

The Attempt at a Solution



Aren't all fixed points going to map to themselves? So shouldn't it be solving for m(z) = z and coming up with roots of a quadratic equation?
 
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Well, I don't know what "it" should be doing but that is what I recommend you do.
 
I meant I* lol. Thanks.
 

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