Find a conformal map of the sector onto the open unit disk mapping 0 to -1 and to +1. Sketch the images of radial lines and of arcs of circles centered at 0. Is the map unique?
The back of the book says that , for any works. Though the map is not unique, the sketch is. I do not see how they got this map. Also, why isn't this map unique? I do not see why. Thank you.