What is the value of `1+w+w^(2)`?

What is the value of |(1,omega,2 omega^(2)),(2,2omega^(2),4 omega^(3)),(3,3 omega^(3),6 omega^(4))| , where omega is the cube root of the unity ?

What is the value of |(1-i, omega^2,-omega), (omega^2+i,omega,-i), (1-2i-omega^2,omega^2-omega,i-omega)|, where omega is the cube root of unity?

If omega is a complex cube root of unity, then what is the value of 1-(1)/((1+omega))-(1)/((1+omega^(2))) ?

What is the value of |{:(1,omega,2omega^(2)),(2,2omega^(2),4omega^(3)),(3,3omega^(3),6omega^(4)):}| , where omega is the cube root of unity ?

What is the value of |{:(" "1-i," "omega^(2)," "-omega),(" "omega^(2)+i," "omega," "-i),(1-2i-omega^(2),omega^(2)-omega,i-omega):}| , where omega is the cube root of unity ?

If w=cos""(pi)/(n)+isin""(pi)/(n) then value of 1+w+w^(2)+.......+w^(n-1) is :