1

**MAT334--Lectures & Home Assignments / Re: FE Sample Question 4 (a)**

« **on:**December 08, 2018, 05:36:32 PM »

Can you approach this method another way without the hint?

I.e) using the three fixed points (choose the last one to be any point that matches the conditions)

Can we choose the third point on the boundary of the domain and image (in this case, both are the unit circle itself), like f(1) = 1?

I don't think you can because in that way you will get a mobius transformation that

$1 \mapsto 1, 0 \mapsto 5, -1 \mapsto -1$, this set of constraints can also be interpreted as the circle passing $1,0,-1$ is mapped to a circle passing $1, 5, -1$, which doesn't satisfy the question?

Using $w_{3} = z_{3} = 1$ as the third point in the triple gives the same answer... maybe it's just luck?