Home
Class 12
MATHS
If 1,alpha(1),alpha(2),......alpha(3n) b...

If `1,alpha_(1),alpha_(2),......alpha_(3n)` be the roots of equation `z^(3n+1)-1=0 and omega` be an imaginary cube root of unity , then `((omega^(2)-alpha_(1))(omega^(2)-alpha_(2))......(omega^(2)-alpha_(3n)))/((omega-alpha_(1))(omega-alpha_(2))......(omega-alpha_(3n)))`

Promotional Banner

Similar Questions

Explore conceptually related problems

If 1,alpha_1,alpha_2,alpha_3,.........,alpha_(3n) be the roots of the eqution x^(3n+1) - 1 =0 , and w be an imaginary cube root of unity, then ((w^2-alpha_1)(w^2-alpha_2)....(w^(3n)-alpha_(3n))) /((w-alpha_1)(w2-alpha)....(w-alpha_(3n)))

If omega be an imaginary cube root of unity, show that (1+omega-omega^2)(1-omega+omega^2)=4

If omega be an imaginary cube root of unity, show that (1+omega-omega^2)(1-omega+omega^2)=4

If omega be an imaginary cube root of unity, show that 1+omega^n+omega^(2n)=0 , for n=2,4

If 1,x_(1),x_(2),x_(3) are the roots of x^(4)-1=0andomega is a complex cube root of unity, find the value of ((omega^(2)-x_(1))(omega^(2)-x_(2))(omega^(2)-x_(3)))/((omega-x_(1))(omega-x_(2))(omega-x_(3)))

If omega is an imaginary cube root of unity, then show that (1-omega)(1-omega^2)(1-omega^4) (1-omega^5)=9

If omega be an imaginary cube root of unity, show that: 1/(1+2omega)+ 1/(2+omega) - 1/(1+omega)=0 .

If alpha is an imaginary fifth root of unity, then log_(2)|1+alpha+alpha^(2)+alpha^(3)-1/alpha|=

If omega is an imaginary cube root of unity, then find the value of (1+omega)(1+omega^2)(1+omega^3)(1+omega^4)(1+omega^5)........(1+omega^(3n))=

if alpha and beta are imaginary cube root of unity then prove (alpha)^4 + (beta)^4 + (alpha)^-1 . (beta)^-1 = 0