Complex Squaring
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This animation shows the action of the complex squaring function ƒ(z) = z2
in the complex plane.
(See notes below.)
If z = x + i y is a complex number, with x and y both
real, then z2 =
(x2 – y2) + 2 i x y.
This animation shows how to visualize the squaring function as a continuous deformation of
the identity function id(z) = z into the squaring function. This deformation is given by
H(t, z) = (1 – t) z + t z2, with
t changing continuously from 0 at the beginning to 1 at the end.
(12/01/07)