Let’s say I want to model: A rotation by π/2, a translation up 2 units and left 3 units, a dilation by a factor of 2 and an inversion. I got: $i(2(1/z)-3+2i) = 2i/z-3i-2=(-3iz-2z+2i)/z$ with z being the variable. Did I do this correctly?
Edit: I can do simple examples like 90 degree rotation: $iz$ or a translation 5 units up then a dilation of 2: $2z+10$