Complex Inversion III
If the animation does not appear, click
here.
This animation shows the action of the complex reciprocal function ƒ(z) = 1 ⁄ z
in the complex plane.
(See notes below.)
If z = x + i y is a non-zero complex number, with x and y both
real, then 1 ⁄ z = (x – i y) ⁄ (x2 + y2).
In this animation, the picture on the left side shows a pair of moving coordinate lines, one red and one
blue. The right-hand picture shows the images, with colors preserved, of those coordinate lines under
the complex inversion function.
See also
Complex Inversion I
and
Complex Inversion II.(12/01/07)