Two points z and z^S element C^* are symmetric with respect to a circle or straight line L if all circles and straight lines passing through z and z^S are orthogonal to L. Möbius transformations preserve symmetry. Let a straight line be given by a point z_0 and a unit vector e^(i θ), then z^S = e^(2i θ) (z - z_0)^_ + z_0, where z^_ is the complex conjugate. Let a circle be given by center z_0 and radius r, then z^S = z_0 + r^2/((z - z_0)^_).