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Complex Number Operations

Constants

0 := 0R+0Ri; 1 := 1R+0Ri; 2 := 2R+0Ri; i := 0R+1Ri.

Arithmetic

x + y := (x0 +R y0) + (x1 +R y1)i;

x - y := (x0 -R y0) + (x1 -R y1)i;

x * y := ((x0 *R y0)-R(x1 *R y1)) + ((x0 * R y1)+R(x1 *R y0))i

x / y := (((x0 *R y0) +R (x1 *R y1)) /R d) +

(((x1 *R y0) -R (x0 * R y1)) /R d)i

where d = (y0 *R y0) +R (y1 *R y1).