Imaginary summation?

Algebra Level 5

If \(n\) is an integer and \(\omega\) is an imaginary cube root of unity, let \(A\) denote the value of

\[{\displaystyle\sum_{k=0}^{n} \binom{n}{k} \omega^{k}}\]

Then the number of possible values of \(e^A \) is?

Note:This question is a part of set KVPY 2014 SB

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