`|[1,w^6,w^8],[w^6,w^3,w^7],[w^8,w^7,1]|`

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

If omega is the cube root of unity then find the value of |[1,omega^(6),omega^(8)],[omega^(6),omega^(3),omega^(7)],[omega^(8),omega^(7),1]|

Let w be the 7^(th) root of unity then log_(3)|1+w+w^(2)+w^(3)+w^(4)+w^(5)-(8)/(w)|=

Let omega be the solution of x^(3)-1=0 with "Im"(omega) gt 0 . If a=2 with b and c satisfying [abc][{:(1,9,7),(2,8,7),(7,3,7):}]=[0,0,0] , then the value of 3/omega^(a) + 1/omega^(b) + 1/omega^( c) is equal to

Which of the following cannot be valid assignment of probability for elementary events or outcomes of samples space S={w_1, w_2, w_3, w_4, w_5, w_6, w_7}: Elementary events w_1 w_2 w_3 w_4 w_5 w_6 w_7 i. 0.1 0.01 0.05 0.03 0.01 0.2 0.6 ii. 1/7 1/7 1/7 1/7 1/7 1/7 1/7 iii. 0.7 0.6 0.5 0.4 0.3 0.2 0.1 iv. 1/(14) 2/(14) 3/(14) 4/(14) 5/(14) 6/(14) (15)/(14)

If the cube roots of unity are 1,omega,omega^(2), then the roots of the equation (x-1)^(3)+8=0 are : (a)-1,1+2w,1+2w^(2)(b)-1,1-2w,1-2w^(2)(b)1,w,w^(2)

|[1,omega,omega^2] , [omega, omega^2,1] , [omega^2,1,omega]|=0

Solve: /_\ = |[omega^(3),omega^(4),omega^(5)],[omega^(6),omega^(8),omega^(2)],[omega^(7),omega^(9),omega]|

If w is an imaginary cube root of unity then prove that (1-w+w^2)(1-w^2+w^4)(1-w^4+w^8)....... " to " 2n "factors" =2^(2n) .

|[omega+omega^(2),1,omega],[omega^(2)+1,omega^(2),1],[1+omega,omega,omega^(2)]|