Complex Inversion II
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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 = (x – i y) ⁄ (x2 + y2).
This animation shows, on the left, a multi-colored grid moving across a portion of the complex plane. At every instant,
the picture on the right shows the image of this grid under the reciprocal map. Notice how the horizontal
and vertical line segments of the grid on the left (almost always) become circular arcs in the image on the right.
See also
Complex Inversion I
and
Complex Inversion III.
(12/01/07)