If ` x=a+b, y=aomega+bomega^2 and z=aomega^2+bomega` where `omega` is an imaginary cube root of unity, prove that `x^2+y^2+z^2=6ab`.

If x=p+q,y=p omega+q omega^(2), and z=p omega^(2)+q omega where omega is a complex cube root of unity then xyz=

If x=a+b,y=aw+bw^(2) and z=aw^(2)+bw, where w is an imaginary cube. root of unity,prove that x^(2)+y^(2)+z^(2)=6ab

If w be an imaginary cube root of unity, prove that (1-w+w^2)^2+(1+w-w^2)^2=-4

If =a+b,y=aomega+bomega^2 and z=aomega^2+bomega, prove tht xyz=a^3+b^3

Prove that a^3 + b^3 + c^3 – 3abc = (a + b + c) (a + bomega + comega^2) (a + bomega^2 + "c"omega) , where omega is an imaginary cube root of unity.

Evaluate: | (1, 1, 1), (1, omega^2, omega), (1, omega, omega^2)| (where omega is an imaginary cube root unity).

If omega be an imaginary cube root of unity, show that 1+omega^n+omega^(2n)=0 , for n=2,4 .

The value of (a+bomega+comega^2)/(b+comega+aomega^2)+(a+bomega+comega^2)/(c+aomega+bomega^2) (where 'omega' is the imaginary cube root of unity), is a.-omega b. omega^2 c. 1 d. -1

If omega is the imaginary cube root of unity, then what is (2-omega+2omega^(2))^(27) equal to ?