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Question

If ω is an imaginary cube root of unity then expression 1.(2ω)(2ω2)+2(3ω)(3ω2)+.....+(n1)(nω)(nω2) is equal to

A
14n2(n+1)2+n
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B
14n2(n+1)2n
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C
14n2(n+1)+n
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D
14n(n+1)2n
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Solution

The correct option is B 14n2(n+1)2n
1.(2w)(2w2)+2(3w)(3w2).......+(n1)(nw)(nw2)
using hit and trial method,
put n=2 and check for the answer.
(2w)(2w2)
2(2w2)w(2w2)
42w22w+w3
52(w2+w)
52(1)
5+2
7

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