omega is an imaginary root of unity. ...

`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`.

Similar Questions

Explore conceptually related problems

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 If a+b+c = 0 then prove that (a + bomega + comega^(2))^(3)+(a+bomega^(2) + comega)^(3) = 27abc .

prove that , (a+bomega+comega^(2))^(3)+(a+bomega^(2)+comega)^(3)=27abc if a+b+c=0.

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)

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

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

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)

If omega is the imaginary cube root of unity and a+b+c=0 then show that (a+bomega+comega^2)^3+(a+bomega^2+comega)^3=27abc

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

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