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

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

If x=omega-omega^2-2 then , the value of x^4+3x^3+2x^2-11x-6 is (where omega is a imaginary cube root of unity)

If x=omega-omega^2-2 then , the value of x^4+3x^3+2x^2-11x-6 is (where omega is a imaginary cube root of unity)

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

If omega be an imaginary cube root of unity, show that (1+omega-omega^2)(1-omega+omega^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 p=a+bomega+comega^2 , q=b+comega+aomega^2 , and r=c+aomega+bomega^2 , where a ,b ,c!=0 and omega is the complex cube root of unity, then (a) p+q+r=a+b+c (b) p^2+z^2+r^2=a^2+b^2+c^2 (c) p^2+z^2+r^2=-2(p q+q r+r p) (d) none of these

The value of the expression 1.(2-omega).(2-omega^2)+2.(3-omega)(3-omega^2)+.+(n-1)(n-omega)(n-omega^2), where omega is an imaginary cube root of unity, is………

If 1, omega, omega^(2) are three cube roots of unity, prove that (1- omega- omega^(2))^(6)= 64