(1) If `w` is cubes of unity then `x=a+b, y =aw+bw^2, z=aw^2+bw` then find `xyz`

If omega is a cube root of unity, then omega + omega^(2)= …..

If omega is a cube root of unity, then 1+ omega^(2)= …..

If omega is a cube root of unity , then |(x+1 , omega , omega^2),(omega , x+omega^2, 1),(omega^2 , 1, x+omega)| =

If omega is a cube root of unity and /_\ = |(1, 2 omega), (omega, omega^2)| , then /_\ ^2 is equal to (A) - omega (B) omega (C) 1 (D) omega^2

If w is a complex cube root of unity then show that ( 2 − w ) ( 2 − w^2 ) ( 2 − w^10 ) ( 2 − w^11 ) = 49 ?

If omega is a cube root of unity, then find the value of the following: (1+omega-omega^2)(1-omega+omega^2)

If w is an imaginary cube root of unity, find the value of |[1,w, w^2],[ w ,w^2 ,1],[w^2 ,1,w]| .

If omega is a cube root of unity, then find the value of the following: (1-omega)(1-omega^2)(1-omega^4)(1-omega^8)

If 1, omega, omega^(2) are cube roots of unity, prove that 1, omega, omega^(2) are vertices of an equilateral triangle

If omega ne 1 is a cube root of unity and a+b=21 , a^(3)+b^(3)=105 , then the value of (aomega^(2)+bomega)(aomega+bomega^(2)) is be equal to