An isogonal mapping is a transformation w = f(z) that preserves the magnitudes of local angles, but not their orientation. A few examples are illustrated above. A conformal mapping is an isogonal mapping that also preserves the orientations of local angles. If w = f(z) is a conformal mapping, then w = f(z^_) is isogonal but not conformal. This is due to the fact that complex conjugation is not an analytic function.

complex conjugate | conformal mapping | indirectly conformal mapping