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Question

If 1,a1,a2...,anāˆ’1 are nth roots of unity, then 11āˆ’a1+11āˆ’a2+...+11āˆ’anāˆ’1 equals

A
2n1n
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B
n12
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C
nn1
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D
None of these
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Solution

The correct option is B n12
Given zn=1,z=1,a1,a2,...,an1
Let a=11zz=11a
(11a)n=1
(a1)nan=0
C1an1+C2an2+...+(1)n=0 where a=11a1,11a2.....11an1
11a1+11a2+.....+11an1=nc2n=n12

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