example of conformal mapping

Consider the four curves A={t}, B={t+it}, C={it} and D={-t+it}, t[-10,10]. Suppose there is a mapping f: which maps A to D and B to C. Is f conformal at z0=0? The size of the angles between A and B at the point of intersection z0=0 is preserved, however the orientation is not. Therefore f is not conformal at z0=0. Now suppose there is a functionMathworldPlanetmath g: which maps A to C and B to D. In this case we see not only that the size of the angles is preserved, but also the orientation. Therefore g is conformal at z0=0.

Title example of conformal mappingMathworldPlanetmathPlanetmath
Canonical name ExampleOfConformalMapping
Date of creation 2013-03-22 13:36:36
Last modified on 2013-03-22 13:36:36
Owner Johan (1032)
Last modified by Johan (1032)
Numerical id 6
Author Johan (1032)
Entry type Example
Classification msc 30E20
Related topic CategoryOfRiemannianManifolds