Thread: Mobiust transformations

Find a Mobius Transformation that takes the circle modulus z=1 to the straight line x+y=1.
I know I need to pick 3 points, but I don't know what to do then. Like if I pick out the point (0,0) or (0,i) do I plug these values into x+y=1. I'm just really confused on this step.

Originally Posted by kathrynmath

Find a Mobius Transformation that takes the circle modulus z=1 to the straight line x+y=1.
I know I need to pick 3 points, but I don't know what to do then. Like if I pick out the point (0,0) or (0,i) do I plug these values into x+y=1. I'm just really confused on this step.

Here is an easier way to do it. The function takes the circle to the line . The function takes the line to . The function takes the line to , which is the desired line. Thus, is a Mobius transformation which does this mapping.

Here is an interesting thread on this topic.