If `13=(13w)/(1-w),` then `(2w)^2=\ ?` (a) `1/4` (b) `1/2\ ` (c) 1 (d) 2

If omega=(-1+sqrt(-3))/(2) , then (1)/(1+omega)+(1)/(1+omega^(2))= (a) 0 (b) - 1 (c) 1 (d) 2w

If omega!=1 is a cube root ofunity satisfying (1)/(a+w)+(1)/(b+w)+(1)/(c+w)=2w^(2) and (1)/(a+w^(2))+(1)/(b+w^(2))+(1)/(c+w^(2))=2u then the value of (1)/(a+1)+(1)/(b+1)+(1)/(c+1) is 2(B)-2(C)omega^(2)(D)omega

(1-w^2+w^4)(1+w^2-w^4)

If 1 , omega , omega^(2) are the cube roots of unity then the values ((a+b omega+c omega^(2))/(c+a omega+b omega^(2))) + ((a+b omega+c omega^(2))/(b+c omega+a omega^(2))) = (A) 1 (B) 0 (C) -1 (D) None of these

If omega be a nth root of unity, then 1+omega+omega^2+…..+omega^(n-1) is (a)0(B) 1 (C) -1 (D) 2

Evaluate the integral,x=int_(0)^((pi)/(4))(1-sin omega t)dt (A) (pi-1)/(omega) (B) (pi-2)/(omega) (C) (pi+1)/(omega) (D) (pi+2)/(omega)

If omega is a complex cube root of unity then the value of determinant |[2,2 omega,-omega^(2)],[1,1,1],[1,-1,0]|= a) 0 b) 1 c) -1 d) 2

(2 + omega + omega ^ (2)) ^ (3) + (1 + omega-omega ^ (2)) ^ (3) = (1-3 omega + omega ^ (2)) ^ (4) = 1

If omega is a non-real cube root of unity, then Delta = |(a_(1) + b_(1) omega,a_(1) omega^(2) + b_(1),a_(1) + b_(1) + c_(1) omega^(2)),(a_(2) + b_(2) omega,a_(2) omega^(2) + b_(2),a_(2) + b_(2) omega + c_(2) omega^(2)),(a_(3) + b_(3) omega,a_(3) omega^(2) + b_(3),a_(3) + b_(3) omega + c_(3) omega^(2))| is equal to