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) Una primera aproximación a estas transformaciones. Representación de dos haces coaxiales de circunferencias ortogonales.
	The Complex Exponential Function The Complex Exponential Function extends the Real Exponential Function to the complex plane.
	Multifunctions: Powers with fractional exponent The usual definition of a function is restrictive. We may broaden the definition of a function to allow f(z) to have many differente values for a single value of z. In this case f is called a many-valued function or a multifunction.
	More about complex functions Examples of complex functions: polynomials, rationals and Moebius Transformations.