If `omega` be an imaginary cube root of unity, show that ` (a+bomega+comega^2)/(aomega+bomega^2+c) = omega^2`

If omega be an imaginary cube root of unity, show that (1+omega-omega^2)(1-omega+omega^2)=4

If omega be an imaginary cube root of unity, show that (1+omega-omega^2)(1-omega+omega^2)=4

If omega be an imaginary cube root of unity, show that (1+omega-omega^(2))(1-omega+omega^(2))=4

If omega be an imaginary cube root of unity,show that (1+omega-omega^(2))(1-omega+omega^(2))=4

If omega is an imaginary cube root of unity, show that (a+ bomega+comega^(2))/(b+comega+aomega^(2))+(a+bomega+comega^(2))/(c+av+bomega^(2))=-1

If omega be an imaginary cube root of unity, show that (xomega^(2)+yomega+z)/(xomega+y+zomega^(2))=omega

If omega is a cube root of unity, prove that (a+bomega+comega^2)/(c+aomega+bomega^2)=omega^2

(a+bomega+comega^(2))/(c+aomega+bomega^(2))

If omega be an imaginary cube root of unity, show that 1+omega^n+omega^(2n)=0 , for n=2,4

If omega is an imaginary cube root of unity, prove that, (a+bomega+comega^(2))^(3)+(a+bomega^(2)+comega)^(3)=(2a-b-c)(2b-c-a)(2c-a-b)