We know that conformal mappings preserve angles and orientation of any two intersecting curves in the z-plane.
Is this fact alone enough to conclude that the region (domain?) to the right of some clockwise-oriented closed curve will again be to the right of the image curve in the w-plane?
This would be as convenient as symmetry arguments of, say, LFTs, but I am not used to using orientation-preserving arguments, so I just wanted to be sure.
Thanks,