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Proof (Continued)

We also have

cartesian(x) *C cartesian(y) =
(x0cos(x1) + x0sin(x1)i) *C (y0cos(y1) + y0sin(y1)i) =
(x0y0cos(x1)cos(y1) - x0y0sin(x1)sin(y1)) +
(x0y0cos(x1)sin(y1) + x0y0sin(x1)cos(y1))i =
x0y0(cos(x1)cos(y1) - sin(x1)sin(y1)) +
x0y0(cos(x1)sin(y1) + x0y0sin(x1)cos(y1))i
We assume the knowledge
cos(x1+y1)= cos(x1)cos(y1) - sin(x1)sin(y1)
sin(x1+y1)= cos(x1)sin(y1) + sin(x1)cos(y1)
as granted and are therefore done.
Author: Wolfgang Schreiner
Last Modification: December 7, 1999

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