TITLE: Finding the Fixed points of a Möbius Transformation
QUESTION [4 upvotes]: Is there a method or algorithm that can be used to find the Fixed points of a Möbius transformation on $\mathbb{C}$?

REPLY [7 votes]: For
$$
f(z)=\frac{az+b}{cz+d}
$$
the fixed points are the solutions of
$$
\frac{az+b}{cz+d}=z
$$
i.e.
$$
cz^2+(d-a)z-b=0
$$
a quadratic in $z$
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