Home
Class 12
MATHS
If 1,alpha1, alpha2, …alpha(n-1) be n, n...

If `1,alpha_1, alpha_2, …alpha_(n-1)` be n, nth roots of unity show that `(1-alpha_1)(1-alpha_2).(1-alpha(n-1)=m`

Answer

Step by step text solution for If 1,alpha_1, alpha_2, …alpha_(n-1) be n, nth roots of unity show that (1-alpha_1)(1-alpha_2).(1-alpha(n-1)=m by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

Doubtnut Promotions Banner Mobile Dark
|

Similar Questions

Explore conceptually related problems

If 1,alpha_1, alpha_2, …alpha_(n-1) be nth roots of unity then (1+alpha_1)(1+alpha_2)……....(1+alpha_(n-1))= (A) 0 or 1 according as n is even or odd (B) 0 or 1 according as n is odd or even (C) n (D) -n

If 1,alpha_(1),alpha_(2),...,alpha_(n-1) are the nth roots of unity,prove that (1-alpha_(1))(1-alpha_(2))...(1-alpha_(n-1))=n. Deduce that sin(pi)/(n)sin(2 pi)/(n)...sin((n-1)pi)/(n)=sin(n)/(2^(n-1))

Knowledge Check

  • If 1,alpha_(1),alpha_(2),………..,alpha_(n-1) are nk^(th) roots of unity, then the value of (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))……(1-alpha_(n-1)) is equal to

    A
    `sqrt(3)`
    B
    `1//2`
    C
    n
    D
    0

  • If 1, alpha_(1), alpha_(2),·····, alpha_(n -1) are the n^(th) roots of unity, then (2-alpha_(1)),(2-alpha_(2))…..(2-alpha_(n-1))=

    A
    n
    B
    `2^(n)`
    C
    `2^(n)+1`
    D
    `2^(n)-1`

  • If 1,alpha,alpha^(2),……….,alpha^(n-1) are n^(th) root of unity, the value of (3-alpha)(3-alpha^(2))(3-alpha^(3))……(3-alpha^(n-1)) , is

    A
    n
    B
    0
    C
    `(3n-1)/2`
    D
    `(3n+1)/2`

    • Similar Questions

    Explore conceptually related problems

    If 1,alpha_(1),alpha_(2),alpha_(3),...,alpha_(n-1) are n, nth roots of unity, then (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))...(1-alpha_(n-1)) equals to

    If 1,alpha_(1),alpha_(2),...,alpha_(n-1) are n^( th) roots of unity then (1)/(1-alpha_(1))+(1)/(1-alpha_(2))+....+(1)/(1-alpha_(n-1))=

    if alpha_(1),alpha_(2),.... alpha_(8) are the 8 th roots of unity then:

    If 1,alpha_(1),alpha_(2)......alpha_(n-1) are n^(th) roots of unity then (1)/(1-alpha_(1))+(1)/(1-alpha_(2))+......+(1)/(1-alpha_(n-1))=

    If alpha_(1),,alpha_(2),...,alpha_(n) are the roots of equation x^(n)+nax-b=0, show that (alpha_(1)-alpha_(2))(alpha_(1)-alpha_(2))...(alpha_(1)-alpha_(n))=n(alpha_(1)^(n-1)+a)

    Home
    Profile