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 find omega+1/omega +1/omega^2

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

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

If omega(ne 1) is a cube root of unity, then |{:(1,1+omega^(2),omega^(2)),(1-i,-1,omega^(2)-1),(-i,-1+omega,-1):}| equals :

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, show that [[1 , omega, omega^2], [ omega, omega^2, 1],[ omega^2, 1, omega]] [[1],[ omega],[ omega^2]]=[[0],[ 0],[ 0]]