Mobius transform part 1. follow up question is here: https://www.coursehero.com/qa/wait/19207970/

Find a Mobius Transform w = o(z) from D = {|z| 1} to W = flu| 0}, where z = x +iy and w = utiv. (a) Sketch or plot both regions. (b) Write down the simplest Mobius Transform (with 1 in the numerator) that maps to oo the common point of all three parts of the boundary of D. Explain why this is a good idea. Sketch or plot the image of D under this mapping. (c) Apply further transforms to position and scale the resulting region as required to fit W, and hence find the Mobius Transform o(z)