\(The \: Value \: of (\frac{-1}{2}) + \left ( \sqrt{\frac{3i}{2}}\right )^{1000} is\)

(1)

\(\begin{array}{l}\Omega ^{3}\end{array} \)

(2)

\(\begin{array}{l}\Omega ^{2}\end{array} \)

(3)

\(\begin{array}{l}\Omega ^{3} – \Omega\end{array} \)

(4)

\(\begin{array}{l}\Omega\end{array} \)

Solution:

(-1+√(3i))/2 = ω

We know ω3n = 1

(-½)+√(3i)/2)1000 = ω1000

= ω3(333) ω

= ω

Hence option (4) is the answer.

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