`((cos3 theta+i sin3 theta)^(5)(cos theta-i sin theta)^(3))/((cos5 theta+i sin5 theta)^(7)(cos2 theta-i sin2 theta)^(5))`

"(cos theta+i sin theta)^(6)(cos theta-i sin theta)^(-3)

((cos2 theta+i sin2 theta)^(3)(cos3 theta-i sin3 theta)^(5))/((cos3 theta+i sin3 theta)^(2)(cos4 theta+i sin4 theta)^(3))=

((cos2 theta+i sin2 theta)^(3)(cos3 theta-i sin3 theta)^(5))/((cos3 theta+i sin3 theta)^(2)(cos4 theta+i sin4 theta)^(3))=...... a)0 b) Cis (-27 theta) c) Cis (27 theta) d) -Cis (27 theta)

Express the following in a+ib form: ((cos2 theta-i sin2 theta)^(4)(cos4 theta+i sin4 theta)^(-5))/((cos3 theta+i sin3 theta)^(-2)(cos3 theta-i sin3 theta)^(-9))

(cos theta + i sin theta)^3 xx (cos theta-i sin theta)^4=

If we express ((cos 2 theta-i sin 2 theta)^(4)(cos 4 theta+i sin 4 theta)^(-5))/((cos 3 theta+i sin 3 theta)^(-2)(cos 3 theta-i sin 3 theta)^(-9)) in the form of x+i y we get

We express ((cos 2theta -i sin 2theta)^(4) (cos 4theta + i sin 4 theta)^(-5))/((cos 3theta + i sin 3theta)^(-2) (cos 3theta -i sin 3theta)^(-9)) in the form of x+iy , we get

The number of values of theta in (0, pi] , such that (cos theta + i sin theta) (cos 3 theta + i sin 3 theta) (cos 5 theta + i sin 5 theta) (cos 7 theta + i sin 7 theta) (cos 9 theta + i sin 9 theta) = -1 is

((cos theta-i sin theta)^(4))/((sin theta+i cos theta)^(5)) is equal to

((cos theta+i sin theta)^(4))/((sin theta+i cos theta)^(5)) is equal to.