Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If 
are the 
roots of unity, then 
is equal to -
A
B
n
C
-1
D
1
Text Solution
Verified by ExpertsThe correct answer is:
B
Being the roots of unity, 1, α 1 , α 2 , …, α n –1 are the roots of x n – 1 = 0, so that
x n – 1 = (x – 1) (x – α 1 ) (x – α 2 ) …. (x – α n–1 )
⇒ (x – α 1 ) (x – α 2 ) …. (x – α n–1 ) = 
= x n–1 + x n–2 + ….. + x + 1
⇒ (x – α 1 ) (x – α 2 ) ….. (x – α n–1 ) = x n–1 + x n–2 + …. + x + 1.
Putting x =1 in the above equation, we now get
(1 – α 1 ) (1 – α 2 ) …. (1 – α n–1 )
= 
= n.
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