`omega` is an imaginary root of unity. Prove that `(a+bomega+comega^2)^3+(a+bomega^2+comega^)^3` `=(2a-b-c)(2b-a-c)(2c-a-b)dot`

omega is an imaginary root of unity.Prove that (a+b omega+c omega^(2))^(3)+(a+b omega^(2)+c omega)^(3)=(2a-b-c)(2b-a-c)(2c-a-b)

omega is an imaginary root of unity. Prove that (i) ( a + bomega + comega^(2))^(3) + (a+bomega^(2) + comega)^(3) = (2a-b-c)(2b -a -c)(2c -a-b) (ii) If a+b+c = 0 then prove that (a + bomega + comega^(2))^(3)+(a+bomega^(2) + comega)^(3) = 27abc .

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

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

If a+b+c=0 and omega,omega^(2) are imaginary cube roots of unity,then (a+b omega+c omega^(2))^(2)+(a+b omega^(2)+c omega)^(3)=3abc (b) 6abc (c) 9 abc (d) 27 abc

If omega is an imaginary cube root of unity, then the value of |(a,b omega^(2),a omega),(b omega,c,b omega^(2)),(c omega^(2),a omega,c)| , is