wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If 1,a1,a2,...an-1 are the nth roots of unity, then the value of(1-a1)(1-a2)(1-a3)...(1-an-1) is


A

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

12

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

n

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C

n


Explanation for correct option:

Given,

1,a1,a2,...an-1 are the nth roots of unity So,

xn-1=x-1x-a1...x-an-1xn-1x-1=x-a1x-a2...x-an-1xn-1+xn-2+...+x2+x+1=x-a1x-a2...x-an-1

Substitute x=1

1n-1+1n-2+...+12+1+1=1-a11-a2...1-an-1=1+1+1+...+ntimes

⇒ RHS=n

⇒ LHS=1n-1+1n-2+...+12+1+1

⇒ LHS=1+1+...+1+1+1

⇒ LHS=n

⇒ LHS=RHS

Hence option (C) is correct.


flag
Suggest Corrections
thumbs-up
3
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Logarithmic Differentiation
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon