(a+b)^(2)+(a omega+b omega^(2))^(2)+(a omega^(2)+b omega)^(2)=

If 1 , omega , omega^(2) are the cube roots of unity , then find the values of the following . (a+ b)^(3) + ( a omega + b omega ^(2))^(3) + ( a omega^(2) + b omega)^(3)

If 1 , omega , omega^(2) are the cube roots of unity , then (a+ b)^(3) + (a omega + b omega^(2))^(3) + ( a omega^(2) + b omega)^(3) =

(a+b omega+c omega^(2))(a+b omega^(2)+c omega)

If 1 , omega , omega^(2) are the cube roots of unity prove that (a + b) ( a omega + b omega^(2))(aomega^(2) + b omega) = a^(3) + b^(3)

If 1, omega, omega^(2) are three cube roots of unity, show that (a + omega b+ omega^(2)c) (a + omega^(2)b+ omega c)= a^(2) + b^(2) + c^(2)- ab- bc - ca

If 1 , omega + omega^(2) are the cube roots of unity prove that (i) (1 - omega + omega^(2))^(6) + (1 - omega^(2) + omega)^(6) = 128 = ( 1 - omega + omega^(2))^(7) + ( 1 + omega - omega^(2))^(7) (ii) ( a+ b) ( aomega+b omega^(2))( a omega^(2) + b omega) = a^(3) + b^(3) (iii) x^(2) + 4x + 7 = 0 " where " x = omega - omega^(2) - 2 .

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 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 a complex cube root of unity, show that (a+b) + (a omega +b omega^2 )+(a omega^2 +b omega ) =0

If 1, omega and omega^(2) are the cube roots of unity, then (a+b+c) (a+b omega+c omega^(2))(a+b omega^(2) +c omega)=