`(2+omega+omega^2)^3+(1+omega-omega^2)^3=(1-3omega+omega^2)^4=1`

(2+omega+omega^2)^3+(1+omega-omega^2)^8-(1-3omega+omega^2)^4=1

If omega is a non-real cube root of unity, then (1+2omega+3omega^2)/(2+3omega+omega^2)+(2+3omega+omega^2)/(3+omega+2omega^2) is equal to

If omega = (-1+sqrt3i)/2 , find the value of |(1, omega, omega^2),(omega, omega^2, 1),(omega^2, 1 , omega)|

If 1, omega, omega^(2) are three cube roots of unity, prove that (1+ omega- omega^(2))^(3)= (1- omega + omega^(2))^(3)= -8

(1-omega+omega^2)(1-omega^2+omega^4)(1-omega^4+omega^2)…. to 2n Factors = 2^(2n)

If omega is the complex cube of unity, find the value of (1-omega- omega^2)^3 + (1-omega+omega^2)^3

If omega is a cube root of unity, prove that (1+omega-omega^2)^3-(1-omega+omega^2)^3=0

(2 + omega + omega ^ (2)) ^ (3) + (1 + omega-omega ^ (2)) ^ (3) = (1-3 omega + omega ^ (2)) ^ (4) = 1

Let omega=-(1)/(2)+i(sqrt(3))/(2), then value of the determinant [[1,1,11,-1,-omega^(2)omega^(2),omega^(2),omega]] is (a) 3 omega(b)3 omega(omega-1)3 omega^(2)(d)3 omega(1-omega)