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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. 2B. 3C. 4D. 6 |
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Answer» Correct Answer - 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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