Question

Find the square root of the following complex number:

2(1 – √3 i)

Answer 1

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 = \(-\frac{\sqrt3}a\)