# Mobius Transformations

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.

© BrainMass Inc. brainmass.com June 3, 2020, 8:05 pm ad1c9bdddfhttps://brainmass.com/math/functional-analysis/mobius-transformations-example-problem-123078

#### Solution Preview

Proof:

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, ...

#### Solution Summary

A Mobius transformation is investigated. The solution is detailed and well presented.

$2.19