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Find the square root of the following complex number: -8 - 6i

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Let \(\sqrt{-8-6i}\) = a + bi, where a, b ∈ R.

Squaring on both sides, we get

-8 – 6i = (a + bi)2

-8 – 6i = a2 + b2 i2 + 2abi

-8 – 6i = (a2 – b2 ) + 2abi …..[∵ i2 = -1]

Equating real and imaginary parts, we get

a2 – b2 = -8 and 2ab = -6

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