# Find the square root of the following complex number: 3 + 2√10 i

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Find the square root of the following complex number:

3 + 2√10 i

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Let $\sqrt{3+2\sqrt{10}i}$ = a + bi, where a, b ∈ R.

Squaring on both sides, we get

3 + 2√10 i = a2 + b2 i2+ 2abi

3 + 2√10 i = (a2 – b2 ) + 2abi ……[∵ i2 = -1]

Equating real and imaginary parts, we get

a2 – b2 = 3 and 2ab = 2√10