`4(3w+2)-5(6w-1)=2(w-8)-6(7w-4)+4`

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

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

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)

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 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) .

If1,w,w^(2) be three cube roots of 1, show that: (1+w-w^(2))(1-w+w^(2))=4 and (3+w+3w^(2))^(6)=64

If omega ne 1 is a cube root of unity, show that (i) (1-omega+omega^(2))^(6)+(1+omega-omega^(2))^(6)=128 (ii) (1+omega)(1+omega^(2))(1+omega^(4))(1+omega^(8))…2n terms=1

If omega is a non-real complex cube root of unity and (5+3 omega^(2)-5 omega)^(4n+3)+(5 omega+3-5 omega^(2))^(4n+3)+(5 omega^(2)+3 omega-5)^(4n+3)=0 then possible value of n is

(3 - omega) ( 3- omega^(2)) ( 3- omega^(4)) (3 - omega^(8)) =