`omega_1=1/2+isqrt3/2 and omega_2=-1/2-i sqrt3/2,` show that `omega_1^2=omega_2.`

if omega=(-1+sqrt(3)i)/(2), then arg(omega^(2)) is

If omega=(-1+i sqrt(3))/(2) then (3+omega+3 omega^(2))^(4)=

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

If omega = frac{-1+sqrt(3)i}{2} , then (3+omega+3(omega)^2)^4 =

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 a complex cube root of unity, show that (2+omega+omega^2)^3 - (1-3omega+omega^2)^3 =65

If 1, omega, omega^2 be three roots of 1, show that: (1+omega)^3-(1+omega^2)^3=0

If 1, omega, omega^2 be three roots of 1, show that: (1+omega)^3-(1+omega^2)^3=0

If omega is a complex cube root of unity,show that ([1 omega omega^(2)omega omega^(2)1 omega^(2)1 omega]+[omega omega^(2)1 omega^(2)1 omega omega omega^(2)1])[1 omega omega^(2)]=[000]

If 1, omega, omega^2 be three roots of 1, show that: (3+omega+3omega^2)^6=64