Complex Inversion III

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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 = (xi 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)