If 1,alpha(1),alpha(2),alpha(3),...,alph...

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

`-n`

`(1)/(2){1-(-1)^(n)}`

None of these

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

COMPLEX NUMBERS
VMC MODULES ENGLISH|Exercise NUMRICAL VALUE TYPE FOR JEE MAIN|14 Videos
COMPLEX NUMBERS
VMC MODULES ENGLISH|Exercise JEE ARCHIVE|76 Videos
COMPLEX NUMBERS
VMC MODULES ENGLISH|Exercise LEVEL - 1|90 Videos
CIRCLES
VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos
CONIC SECTIONS
VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

Similar Questions

Explore conceptually related problems

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

If alpha_(0),alpha_(1),alpha_(2),...,alpha_(n-1) are the n, nth roots of the unity , then find the value of sum_(i=0)^(n-1)(alpha_(i))/(2-a_(i)).

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^(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, ,alpha_2, ,alpha_n are the roots of equation x^n+n a x-b=0, show that (alpha_(1)-alpha_(2))(alpha_(1)-alpha_(3))...(alpha_(1)-alpha_(n))=nalpha_(1)^(n-1)+nalpha

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 alpha_(1),alpha_(2),alpha_(3), alpha_(4) are the roos of x^(4)+2x^(3)+bx^(2)+cx+d=0 such that alpha_(1)-alpha_(3)=alpha_(4)-alpha_(2) , then b-c is equal to__________

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

VMC MODULES ENGLISH-COMPLEX NUMBERS -LEVEL - 2

The value of (a+bomega+comega^2)/(b+comega+aomega^2)+(a+bomega+comega^...
Text Solution
|
For a complex number z the minimum value of |z|+|z-cos alpha-i sin alp...
Text Solution
|
If 1,alpha(1),alpha(2),alpha(3),...,alpha(n-1) are n, nth roots of uni...
Text Solution
|
If k>0, |z|=|w|=k, and alpha=(z-bar w)/(k^2+zbar(w)), then Re(alpha) ...
Text Solution
|
If |z-1|=1, where z is a point on the argand plane, show that(z-2)/(z)...
Text Solution
|
Let 1, z(1),z(2),z(3),…., z(n-1) be the nth roots of unity. Then pro...
Text Solution
|
If the roots of (z-1)^n=i(z+1)^n are plotted in ten Arg and plane, the...
Text Solution
|
If for complex numbers z1 and z2 and |1-bar(z1)z2|^2-|z1-z2|^2=k(1-|z1...
Text Solution
|
If |a(i)|lt1lamda(i)ge0 for i=1,2,3,.......nandlamda(1)+lamda(2)+........
Text Solution
|
if (tanalpha-i(sin ""(alpha)/(2)+cos ""(alpha)/(2)))/(1+2 i sin ""(alp...
Text Solution
|
If sqrt(1-c^(2))=nc-1andz=e^(itheta)," then "(c)/(2n)(1+nz)(1+(n)/(z))...
Text Solution
|
If z=x+iy,x,y real , then |x|+|y|lek|z| where k is equal to :
Text Solution
|
If arg(z)=-pi/4 then the value of arg((z^5+(bar(z))^5)/(1+z(bar(z))))^...
Text Solution
|
If p/a + q/b + r/c=1 and a/p + b/q + c/r=0, then the value of p^(2)/a^...
Text Solution
|
If cosA+cosB+cosC=0,sinA+sinB+sinC=0andA+B+C=180^(@) then the value of...
Text Solution
|
Let |(barZ(1) - 2barz(2))//(2-z(1)barz(2))|= 1 and |z(2)| ne 1, where...
Text Solution
|
Let z be a complex number having the argument theta ,0 < theta < pi/2,...
Text Solution
|
If |z+2-i|=5 and maxium value of |3z +9-7i| is M, then the value of M ...
Text Solution
|
If a, b are complex numbers and one of the roots of the equation x^(2)...
Text Solution
|
Solve for z : z^2-(3-2i)z=(5i-5)dot
Text Solution
|