If 1,a(1), a(2). ..., a(n-1) are n roots...

If 1,`a_(1), a_(2). ..., a_(n-1)` are n roots of unity, then the value of `(1 - a_(1)) (1 - a_(2)) .... (1 - a_(n-1)) ` is :

`2^(n)`

`2^(n)+1`

`2^(n)-1`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

COMMON ENTRANCE TEST -2016
HIMALAYA PUBLICATION|Exercise QUESTION BANK|60 Videos
COORDINATE SYSTEMS, LOCUS AND STRAIGHT LINES
HIMALAYA PUBLICATION|Exercise QUESTION BANK|297 Videos

Similar Questions

Explore conceptually related problems

If a_(1) , a_(2), "……………" a_(n) are in H.P., then the expression a_(1) a_(2) + a_(2) a_(3)+"…….."+ a_(n-1) a_(n) is equal to :

If a_(1) , a_(2) , a_(3),"…………."a_(n) are in A.P., where a_(i) gt 0 for all i, then the value of : (1) /( sqrt(a_(1))+sqrt(a_(2)))+ (1) /( sqrt(a_(2))+sqrt(a_(3)))+"......"+(1) /( sqrt(a_(n-1))+sqrt(a_(n))) is :

If a_(1) , a_(2),"………",a_(n) are n non-zero real numbers such that ( a_(1)^(2) +a_(2)^(2) + "........."+a_(n-1)^(2) ) ( a_(2)^(2) + a_(3)^(2) + "........"+a_(n)^(2))le(a_(1) a_(2) + a_(2) a_(3) +".........." +a_(n-1) a_(n))^(2), a_(1), a_(2),".........",a_(n) are in :

If a_(1) , a_(2) , a_(3),"………."a_(n) are in H.P. , then a_(1), a_(2) + a_(2) a_(3) + "………" + a_(n-1)a_(n) will be equal to :

If a_(1), a_(2), a_(3)"….." are in G.P. , then the value of Delta= |{:(log a_(n),loga_(n+1),loga_(n+2)),(log a_(n+3),loga_(n+4),loga_(n+5)),(loga_(n+6),loga_(n+7),loga_(n+8)):}| is :

If a_(r ) gt 0, r in N and a_(1), a_(2) , a_(3) ,"……..",a_(2n) are in A.P. then : (a_(1) + a_(2n))/( sqrt( a_(1))+ sqrt(a_(2))) + ( a_(2) + a_(2n-1))/(sqrt(a_(2)) + sqrt(a_(3)))+"......"(a_(n)+a_(n+1))/(sqrt(a_(n))+sqrt(a_(n+1))) is equal to :

If a_(1)=2 and a_(n)=2a_(n-1)+5 for ngt1 , the value of sum_(r=2)^(5)a_(r) is

If a_(1),a_(2) , a_(3),"……..",a_(n) are in H.P. , then : (a_(1))/( a_(2) + a_(3) +"........."+a_(n)),(a_(2))/(a_(1) + a_(3)+"..........."+a_(n)),"......",(a_(n))/(a_(1)+a_(2)+"........"a_(n-1)) are in :

If a_(1),a_(2),a_(3),".....",a_(n) are in HP, than prove that a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+"....."+a_(n-1)a_(n)=(n-1)a_(1)a_(n)

If (1+x+x^(2))^(n) = a_(0)+a_(1) x+a_(2) x^(2)+..+a_(2 n) x^(2 n) then the value of a_(1)+a_(4)+a_(7)+.. . . is

HIMALAYA PUBLICATION-COMPLEX NUMBERS-QUESTION BANK

If z(1)=1+i sqrt(3) , z(2)=1-i sqrt(3), then (z(1)^(100)+z(2)^(100))/(...
Text Solution
|
If z(1)=1+i, z(2)=sqrt(3)+i, then arg ((z(1))/(z(2)))^(50)=
Text Solution
|
If 1,a(1), a(2). ..., a(n-1) are n roots of unity, then the value of (...
Text Solution
|
If z is such that |z-2 i|=2 sqrt(2), then arg ((z-2)/(z+2))=
Text Solution
|
If |z(1)-1|lt2,|z(2)-2|lt1, then |z(1)+z(2)|
Text Solution
|
If z(1) and z(2) are two non-zero complex numbers such that |z(1)+z(2)...
Text Solution
|
The number i^(i) is
Text Solution
|
The complex number z has argument, 0ltthetalt(pi)(2) and satisfy the e...
Text Solution
|
If z(1) and z(2) are two non-zero complex numbers such that |z(1)+z(2)...
Text Solution
|
The inequality |z-4|lt|z-2| represents the region given by
Text Solution
|
The smallest positive integer n for which (1+i sqrt(3))^(n / 2) is rea...
Text Solution
|
If x^(2)+x+1=0, then sum(r=1)^(2005)(x^(r)+(1)/(x^(r)))^(3)=
Text Solution
|
If z(1), z(2), z(3) be vertices of an equilateral triangle occurring ...
Text Solution
|
If z(1), z(2) are two complex numbers such that Im(z(1)+z(2))=0 and Im...
Text Solution
|
If alpha is an imaginary fifth root of unity then log (2)|1+alpha+alph...
Text Solution
|
If |z+bar(z)|+|z-bar(z)|=8 then z lies on
Text Solution
|
The equation |z+i|-|z-i|=k represents a hyperbola, if
Text Solution
|
If |z|=k and w=(z-k)/(z+k), then Re (w)=
Text Solution
|
If z is a complex number satisfying z^(4)+z^(3)+2 z^(2)+z+1=0 then |z|...
Text Solution
|
If alpha is a non-real fifth root of unity, then 3^(|1+alpha+a^(2)+a^(...
Text Solution
|