If `w` is cube roots of unity, `(1-w+w^2)^7+(1+w-w^2)^7`

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

If omega is a cube root of unity, then omega^(3) = ……

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

If omega(!=1) is a cube root of unity, and (1+omega)^7= A + B omega . Then (A, B) equals

If omega is a cube root of unity, then omega + omega^(2)= …..

If 1, omega, omega^(2) are three cube roots of unity, prove that (1- omega) (1- omega^(2))= 3

If w is a complex cube root of unity. Show that |[1,w, w^2],[w, w^2, 1],[w^2, 1,w]|=0 .

If omega is a cube root of unity and /_\ = |(1, 2 omega), (omega, omega^2)| , then /_\ ^2 is equal to (A) - omega (B) omega (C) 1 (D) omega^2

If omega is complex cube root of unity (1-omega+ omega^2) (1-omega^2+omega^4)(1-omega^4+omega^8)(1-omega^8+omega^16)

If w ne 1 is a cube root of unity and Delta=|{:(x+w^(2),w,1),(w,w^(2),1+x),(1,x+w,w^(2)):}|=0 , then value of x is