Maple 9.5 can't recognize exp(+I*phi) = cos(phi) + I*sin(phi)

[bjnartowt]

Homework Statement

((1/2)*sin(theta)*cos(phi) - I*(1/2)*sin(theta)*sin(phi))*exp(+I*phi)

should equal:

(1/2)*sin(theta)

Or:
((1/2)*sin(theta)*cos(phi) + I*(1/2)*sin(theta)*sin(phi))*exp(+I*phi)

should equal:
(1/2)*sin(theta)*exp(+2*I*phi)


I may add: Maple 9.5 cannot make the simplification:
exp(-I*phi)*exp(-I*phi) = exp(-2*I*phi);

...I'm trying to automate Maple recognizing this: use simplify(,trig) and simplify(,size). There does not seem to be a simplify(,euler) or simplify(,complex), where one can teach Maple to recognize that cancellation. It would make my life tons easier if there was a way to do that. It must exist...somewhere?

 

[NateD]

The Attempt at a Solution((1/2)*sin(theta)*cos(phi) - I*(1/2)*sin(theta)*sin(phi))*exp(+I*phi)= (1/2)*sin(theta)*exp(+I*phi)*cos(phi) - (1/2)*sin(theta)*exp(+I*phi)*sin(phi)= (1/2)*sin(theta)*exp(+I*phi)*(cos(phi) - I*sin(phi))= (1/2)*sin(theta)*exp(+I*phi)*exp(-I*phi)= (1/2)*sin(theta)*exp(+I*phi)*exp(-2*I*phi)= (1/2)*sin(theta)*exp(-I*phi)= (1/2)*sin(theta)...so maple is able to make the simplification, just not automatically.