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If n is a positive integer and omegane1 ...

If n is a positive integer and `omegane1` is a cube of unity, the number of possible values of `|e^(sum_(k=0)^(n) ((n)/(k))omega^(k))|`

A

2

B

3

C

4

D

6

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(k-0)overset(n)sum .^(n)C_(k)omega^(k)=""^(n)C_(1)omega+....+""^(c)C_(n)omega^(n)`
`=(1omega)^(n)=(-omega^(2))^(n)`
`(-1)^(n) omega^(2n)`
`:. |e^((-1)^(n)omega^(2n))|=|e^((-omega^(2))^(n))|`
`=|e^(-cos.(npi)/(3)isin""(4pi)/(3))|`
`=|e^(cos.(npi)/(3))|` can have values
`={e^(1),e^(1//2),e^(-1//2),e^(-1)}`
Four values.
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