Symmetric points are preserved under a Möbius transformation. The Schwarz reflection principle is sometimes called the symmetry principle (Needham 2000, p. 252).
Symmetry Principle
See also
Möbius Transformation, Symmetric PointsExplore with Wolfram|Alpha
References
Needham, T. "Analytic Continuation." §5.XI in Visual Complex Analysis. New York: Clarendon Press, pp. 247-257, 2000.Referenced on Wolfram|Alpha
Symmetry PrincipleCite this as:
Weisstein, Eric W. "Symmetry Principle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SymmetryPrinciple.html