Suppose T is a Mobius transformation such that the image of the real axis under T is the real axis. Prove that T may be written in the form T(z) = (az+b)/(cz+d) with a, b, c, and d real.
Since T is a Mobius transformation, we can assume T(z)=(az+b)/(cz+d). Now we want to show that a,b,c,d can be written as all reals.
First, T(0)=b/d=r is a real, then b=rd, ...
A Mobius transformation is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.