Express the following in `a+i b` form: `((cos2theta-isin2theta)^4(cos4theta+isin4theta)^(-5))/((cos3theta+isin3theta)^(-2)(cos3theta-isin3theta)^(-9))`

frac{(cos2theta-isin2theta)^4(cos4theta+isin4theta)^-5}{(cos3theta+isin3theta)^-2(cos3theta-isin3theta)^-9} =

((cos2theta+isin2theta)^(3)(cos3theta-isin3theta)^(4))/((cos3theta+isin3theta)^(2)(cos4theta+isin4theta)^(-3))

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))

(cos3theta+isin3theta)^5/(costheta+isintheta)^6

((costheta+isintheta)^(5)(cos3theta-isin3theta)^(6))/((cos2theta+isin2theta)^(3)(cos4theta-isin4theta)^(5))

Simplify ((cos2theta+isin2theta)^6(cos3theta+isin3theta)^(-5))/((cos5theta+isin5theta)^(-8)(cos6theta-isin6theta)^(-2))

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

Show that, ((cos2theta+isin2theta)^3(cos3theta-isin3theta)^4)/((cos3theta+isin3theta)^2(cos4theta+isin4theta)^(-3))=1

(cos2theta+isin2theta)^(-5)(cos3theta-isin3theta)^(6)(sintheta-icostheta)^(3) is

((costheta+isintheta)^5(cos3theta-isin3theta)^6)/((cos2theta+isin2theta)^3(cos4theta-isin4theta)^5)=