example of conformal mapping
Consider the four curves , , and , . Suppose there is a mapping which maps to and to . Is conformal at ? The size of the angles between and at the point of intersection is preserved, however the orientation is not. Therefore is not conformal at . Now suppose there is a function which maps to and to . In this case we see not only that the size of the angles is preserved, but also the orientation. Therefore is conformal at .