$\sqrt{- 8 - 6 i} =$

\pm

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\pm

(1 - 3i)

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\pm

(1 + 3i)

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\pm

(3 - i)

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Solution

The correct option is A $\pm$ (1 - 3i)
$\sqrt{- 8 - 6 i} = a + i b$
squaring on both sides and comparing real and imaginary parts gives
$\Rightarrow a^{2} - b^{2} = - 8$ and $a b = - 3$
$\Rightarrow a = 1$ and $b = - 3$ or $a = - 1$ and $b = 3$
$∴ \sqrt{- 8 - 6 i} = \pm (1 - 3 i)$
Hence, option B.

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