Let C be the circle with center -3i and radius 2. The Mobius transformation R given by the equation R(z)= b/(z+d) maps C to the unit circle in such a way that the inside of C maps to the outside of the unit circle. Find |R(1-2i)|.

Question

Let C be the circle with center -3i and radius 2. The Mobius transformation R given by the equation R(z)= b/(z+d) maps C to the unit circle in such a way that the inside of C maps to the outside of the unit circle. Find |R(1-2i)|.

Answer 1

Woahhh!, not the pre-Calculus I had dealt with

Found two videos,
https://www.youtube.com/watch?v=48aerHs9wL0

and a second one, which is a terrible presentation,
https://www.youtube.com/watch?v=l19OD7LUkNo

both are beyond my level of expertise, but perhaps you can
get something out of it