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Q.

What is the value of ${(1 - i \sqrt{3})}^{9}$

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a

$2^{9} i$

b

$2^{9}$

c

$- 2^{9} i$

d

$- 2^{9}$

answer is B.

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Detailed Solution

${(1 - i \sqrt{3})}^{9} = {(- 2 w)}^{9} = {(- 2)}^{9} {(w^{3})}^{3} = - 2^{9}$

Since $w = \frac{- 1 + i \sqrt{3}}{2}$

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