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We also have

We assume the knowledge

cartesian( x) *_{C}cartesian(y)= ( x_{0}cos(x_{1}) +x_{0}sin(x_{1})i) *_{C}(y_{0}cos(y_{1}) +y_{0}sin(y_{1})i)= ( x_{0}y_{0}cos(x_{1})cos(y_{1}) -x_{0}y_{0}sin(x_{1})sin(y_{1})) +( x_{0}y_{0}cos(x_{1})sin(y_{1}) +x_{0}y_{0}sin(x_{1})cos(y_{1}))i= x_{0}y_{0}(cos(x_{1})cos(y_{1}) - sin(x_{1})sin(y_{1})) +x_{0}y_{0}(cos(x_{1})sin(y_{1}) +x_{0}y_{0}sin(x_{1})cos(y_{1}))i

as granted and are therefore done.

cos( x_{1}+y_{1})= cos( x_{1})cos(y_{1}) - sin(x_{1})sin(y_{1})sin( x_{1}+y_{1})= cos( x_{1})sin(y_{1}) + sin(x_{1})cos(y_{1})

Author: Wolfgang Schreiner

Last Modification: December 7, 1999