Finding Fixed Points of a Mobius transformation

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To find the fixed points of the Mobius transformation m(z) = (2z + 5)/(3z - 1), one must solve the equation m(z) = z. This leads to the quadratic equation resulting from setting (2z + 5)/(3z - 1) = z. The fixed points are the values of z that satisfy this equation. The discussion emphasizes that fixed points map to themselves, confirming the approach of solving for roots. The recommended method is to derive and solve the quadratic equation.
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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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