`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)

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)

If omega is the imaginary cube root of 1 then prove that (a+bomega+comega^2)^3+(a+bomega^2+comega)^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 .

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 .

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

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

(a-b)(aomega-bomega^(2))(aomega^(2)-bomega)

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