Find the square root of the following complex number: 2(1 – √3 i)

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Find the square root of the following complex number:

2(1 – √3 i)

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Let $\sqrt{2(1-\sqrt3i)}$ = a + bi, where a, b ∈ R.

Squaring on both sides, we get

2(1 – √3 i) = a2 + b2 i2 + 2abi

2 – 2√3 i = (a2 – b2 ) + 2abi ….[∵ i2 = -1]

Equating real and imaginary parts, we get

a2 – b2 = 2 and 2ab = -2√3

a2 - b2 = 2 and b = $-\frac{\sqrt3}a$

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