If `p=a+bomega+comega^2,q=b+comega+aomega^2,a n dr=c+aomega+bomega^2,w h e r ea ,b ,c!=0a n domega` is the complex cube root of unity, then `

(2-omega)(2-omega^(2))(2-omega^(10))(2-omega^(11))="…….." , where omega is the complex cube root of unity

Prove that the value of determinant |{:(1,,omega,,omega^(2)),(omega ,,omega^(2),,1),( omega^(2),, 1,,omega):}|=0 where omega is complex cube root of unity .

If x = a + b, y = a omega + b omega^2, z = aomega^2 + b omega , show that (i) xyz = a^3 + b^3

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………

Prove that a^4+b^4+c^4> a b c(a+b+c),w h e r ea ,b ,c > 0.

If z=omega,omega^2w h e r eomega is a non-real complex cube root of unity, are two vertices of an equilateral triangle in the Argand plane, then the third vertex z may be represented by (a) z=1 b. z=0 c. z=-2 d. z=-1

If omega is a non real cube root of unity, then (a+b)(a+b omega)(a+b omega^2)=

If one root of the equation z^2-a z+a-1=0i s(1+i),w h e r ea is a complex number then find the root.

If omega is a complex cube root of unity, then (a+b omega+c omega^(2))/(c+a omega+b omega^(2))+(c+a omega+b omega^(2))/(a +b omega+c omega^(2))+(b+c omega+a omega^(2))/(b+c omega+a omega^(5))=

If omega pm 1 is a cube root of unity, show that (a + b omega + c omega^(2))/(b + c omega + a omega^(2))+ (a + b omega + c omega^(2))/(c + a omega + b omega^(2)) = -1