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

**Squaring on both sides, we get**

2(1 – √3 i) = a^{2} + b^{2} i^{2} + 2abi

2 – 2√3 i = (a^{2} – b^{2} ) + 2abi …**.[∵ i**^{2} = -1]

**Equating real and imaginary parts, we get**

a^{2} – b^{2} = 2 and 2ab = -2√3

a^{2} - b^{2} = 2 and b = \(-\frac{\sqrt3}a\)