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Consider the graph of the complex identity function w =
z. Here z = x + yi and
w = u + vi where x, y,
u, and v are real variables. We choose as the domain for
z the unit square in the z-plane, given by -1
< x < 1, -1 < y <
1, so the ranges of u and v will also be given by the
same interval. The graph of the identity function will then be a
parallelogram in four-space with its four edges along the diagonals of
four of the square faces of the hypercube.
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