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Question

If 1,ω,ω2,....ωn1 are n,nth roots ofunity then the value of (13ω)(13ωn1) equals

A
13n+13
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B
13n13
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C
13n1
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D
None of these
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Solution

The correct option is B None of these
(13w)(13wn1)
=(13w)(13wnw)
=(13w)(13¯¯¯¯w)
=16913(w+¯¯¯¯w)+w¯¯¯¯w
=16913(Re(w))+1
=17013(Re(w))
Hence answer is none of these.

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