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`1,alpha_1,alpha_2,alpha_3…..alpha_(n-1)` are the `n^(th)` roots of unity and n is an even natural number ,then `(1+alpha_1)(1+alpha_2)(1+alpha_3)….(1+alpha_(n-1))=`

A

only I is true

B

only II is true

C

both I and II are true

D

neither I nor II true

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Knowledge Check

  • If 1,alpha_1,alpha_2,…..alpha_(n-1) are the n^(th) roots of unity and n is an odd natural number then (1+alpha_1)(1+alpha_2)…..(1+alpha_(n-1))=

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    `-1`
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  • If 1,alpha,alpha^2,…...,alpha^(n-1) are the n^(th) roots of unity, then the value of (3-alpha)(3-alpha^2)…...(3-alpha^(n-1)) is

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