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Find the square root of the following complex number: 7 + 24i

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Find the square root of the following complex number: 7 + 24i

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Let \(\sqrt{7+24i}\) = a + bi, where a, b ∈ R.

Squaring on both sides, we get

7 + 24i = (a + bi)2

7 + 24i = a2 + b2 i + 2abi

7 + 24i = (a2 – b2 ) + 2abi …..[∵ i = -1]

Equating real and imaginary parts, we get

a2 – b2 = 7 and 2ab = 24

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