Find the square root of $7 + 24 i$

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Solution

Given $7 + 24 i$
square root $= (7 + 24 i)^{2}$
$= (7 + 24 i) (7 + 24 i)$
$= 49 - (24)^{2} + 7 \times 24 i + 7 + 24 i$
$= 49 - 576 + 48 \times 7 i$
$= - 527 + 336 i$

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