Inversion in a circle is a transformation that preserves the magnitude of angles but each angle is mapped to an angle of opposite sign. The sense or direction of each angle is reversed. Inversion in a circle is an anticonformal mapping (like a reflection in a line).

In particular, inversion is a mapping that preserves the angle of intersection of two circles. Orthogonal circles (or lines) invert into orthogonal circles (or lines). A circle orthogonal to the circle of inversion is mapped into itself.

All the lines through a point and all the circles concentric with the same point as a center can be seen as two particular cases of coaxal sistem of circles. These two coaxal sistems are orthogonal. The lines form a coaxal system of intersecting type and the concentric circles are a non-intersecting coaxal system. These coaxal systems are mapped into two orthogonal coaxal systems:

Every "small" rectangle is transformed into an "small" rectangle:

In this picture we can see how the order of colors is reversed:

LINKS

	Inversion Inversion is a plane transformation that transform straight lines and circles in straight lines and circles.
	Moebius transformations (Spanish)
	The Complex Exponential Function The Complex Exponential Function extends the Real Exponential Function to the complex plane.
	More about complex functions Examples of complex functions: polynomials, rationals and Moebius Transformations.