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

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`

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

If alpha is an n^(th) roots of unity, then 1+2alpha+3alpha^(2)+……..+nalpha^(n-1) equals

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,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

If nge3and1,alpha_(1),alpha_(2),.......,alpha_(n-1) are nth roots of unity then the sum sum_(1leiltjlen-1)alpha_(i)alpha(j)=

If 1,alpha_1,alpha_2, ,alpha_(n-1) are the n t h roots of unity, prove that (1-alpha_1)(1-alpha_2)(1-alpha_(n-1))=ndot Deduce that sinpi/nsin(2pi)/n sin((n-1)pi)/n=n/(2^(n-1))

If 1,alpha,alpha^2,alpha^3,......,alpha^(n-1) are n n^(th) roots of unity, then find the value of (2011-alpha)(2011-alpha^2)....(2011-alpha^(n-1))

If 1,alpha,alpha^(2),.......,alpha^(n-1) are the n^(th) roots of unity, then sum_(i=1)^(n-1)(1)/(2-alpha^(i)) is equal to:

If alpha (!=1) is a nth root of unity then S = 1 + 3alpha+ 5alpha^2 + .......... upto n terms is equal to

If alpha is an imaginary root of z^n -1=0 then 1+alpha+alpha^2+………_+alpha^(n-1)= (A) 1 (B) -1 (C) 0 (D) 2

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