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If 1,z1 ​ ,z2 ​ ,z3 ​ ,...,z(n−1) ​ ...

If `1,z_1 ​ ,z_2 ​ ,z_3 ​ ,...,z_(n−1)` ​ are nth roots of unity, then show that `(1−z_1 ​ )(1−z_2 ​ )...(1−z_(n−1) ​ )=n`

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The correct Answer is:
A
`(a)` Let vertices be `1, alpha,alpha^(2),……….,alpha^(n-1)`
Given `1+alpha+alpha^(2)+…….+alpha^(n-1)=0impliesalpha^(n)-1=0`
`impliesz_(1),z_(2),z_(3),……….,z_(n)` are roots of `alpha^(n)=1`
which form regular polygon. So distance is zero.
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