`(a+b)(aomega+b omega^(2))(aw^(2)+bw)=?`

(a+b) (a omega+b omega^(2)) (aw^(2)+bw) =?

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)

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

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 .

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

If omega is an imaginary cube root of unity, show that (omega)/(9)[(1- omega)(1-omega^(2))(1- omega^(4))(1- omega^(8))+9((c+aomega+bomega^(2))/(aomega^(2)+b+comega))^(2)]=-1

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

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

If omega ne 1" and "omega^(3)=1 , the (a omega+b + c omega^(2))/(a omega^(2)+b omega+c)+(a omega^(2)+b+c omega)/(a+b omega+c omega^(2)) is equal to

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