The product of the distinct (2n)th roots of 1+i3 is equal to

x=-2×-1-i3212n=-2w212n ⇒x2n+2w2=0; product of roots =2w2=-1-i3

The product of the distinct (2n)th roots of 1+i3 is equal to

x=-2×-1-i3212n=-2w212n ⇒x2n+2w2=0; product of roots =2w2=-1-i3

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The product of the distinct (2n)th roots of $1 + i \sqrt{3}$ is equal to

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$1 + i \sqrt{3}$

$- 1 - i \sqrt{3}$

$- 1 + i \sqrt{3}$

answer is B.

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Detailed Solution

$x = {(- 2 \times \frac{- 1 - i \sqrt{3}}{2})}^{\frac{1}{2 n}} = {(- 2 w^{2})}^{\frac{1}{2 n}} \Rightarrow x^{2 n} + 2 w^{2} = 0; p r o d u c t o f r o o t s = 2 w^{2} = - 1 - i \sqrt{3}$

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The product of the distinct (2n)th roots of $1 + i \sqrt{3}$ is equal to