The question is, Find an LFT that maps |z|<=1 onto |w|<=1 so that z=i/2 is mapped onto w=0. Sketch the images of the lines x=const and y=const.
By searching and solving, I found several different solutions.
- $w=\frac{2}{3}(z-\frac{1}{2})$
- $w=\frac{i-2z}{iz+2}$
- $w=\frac{z-i/2}{1-iz/2}$
Which one is the right thing?