Finding Fixed Points of a Mobius transformation

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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.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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