if `omega!=1` is a complex cube root of unity, and `x+iy=|[1,i,-omega],[-I,1,omega^2],[omega,-omega^2,1]|`

If omega is a complex cube root of unity then a root of the equation |[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^2,1,x+omega]|=0 is

If omega is a complex cube root of unity, show that [[1 , omega, omega^2], [ omega, omega^2, 1],[ omega^2, 1, omega]] [[1],[ omega],[ omega^2]]=[[0],[ 0],[ 0]]

If omega is the complex cube root of unity then |[1,1+i+omega^2,omega^2],[1-i,-1,omega^2-1],[-i,-i+omega-1,-1]|=

If omega is the complex cube root of unity then |[1,1+i+omega^2,omega^2],[1-i,-1,omega^2-1],[-i,-i+omega-1,-1]|=

If omega is the complex cube root of unity then |[1,1+i+omega^2,omega^2],[1-i,-1,omega^2-1],[-i,-i+omega-1,-1]|=

If omega is a complex cube root of unity, then (1+omega^2)^4=

If omega is the complex cube root of unity, then find omega+1/omega

If omega is a complex cube root of unity, then (x+1)(x+omega)(x-omega-1)

If omega is a complex cube root of unity, then (1-omega+(omega)^2)^3 =