Sum the series : `1(2-omega)(2-omega^(2))+2(3-omega)(3-omega^(2))......(n-1)(n-omega)(n-omega^(2))` where `omega` and `omega^(2)` are non-real cube roots of unity.

Value of |{:(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,omega):}| is zero, where omega,omega^(2) are imaginary cube roots of unity.

Show that a=r omega^(2) .

If omega(ne1) is a cube root of unity, then (1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8)) …upto 2n is factors, is

If omega^(3)=1 and omega ne1 , then (1+omega)(1+omega^(2))(1+omega^(4))(1+omega^(5)) is equal to

Let omega ne 1 be a complex cube root of unity. If (3-3omega+2omega^(2))^(4n+3) + (2+3omega-3omega^(2))^(4n+3)+(-3+2omega+3omega^(2))^(4n+3)=0 , then the set of possible value(s) of n is are

If omega!=1 is a complex cube root of unity, then prove that [{:(1+2omega^(2017)+omega^(2018)," "omega^(2018),1),(1,1+2omega^(2018)+omega^(2017),omega^(2017)),(omega^(2017),omega^(2018),2+2omega^(2017)+omega^(2018)):}] is singular

If 1,alpha_1,alpha_2,alpha_3,alpha_4 be the roots x^5-1=0 , then value of [omega-alpha_1]/[omega^2-alpha_1].[omega-alpha_2]/[omega^2-alpha_2].[omega-alpha_3]/[omega^2-alpha_3].[omega-alpha_4]/[omega^2-alpha_4] is (where omega is imaginary cube root of unity)

If omega ne 1 and omega^3=1 , then : (a omega+b+c omega^2)/(a omega^2+b omega+c) + (a omega^2+b+c omega)/(a+b omega+c omega^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 x, y, z are not all zero & if ax + by + cz=0, bx+ cy + az=0 & cx + ay + bz = 0 , then prove that x: y : z = 1 : 1 : 1 OR 1 :omega:omega^2 OR 1:omega^2:omega , where omega is one ofthe complex cube root of unity.