Question

Find the square of
$\sqrt{9 + 40 i \ } + \sqrt{9 - 40i}$
​

Answer 1

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$\star \: \underline \blue{solution} \blue{ : }$

$y = \sqrt{9 + 40i} + \sqrt{9 - 40i} \: \: \: \: \: \: \: \: \bold{let}$

$\longrightarrow \: {y}^{2} = {(\sqrt{9 + 40i} + \sqrt{9 - 40i})}^{2}$

$\longrightarrow \: {y}^{2} = 9 + 40i + 9 - 40i + 2 \sqrt{(9 + 40i)(9 - 40i)}$

$\longrightarrow \: {y}^{2} = 18 + 2 \sqrt{1681}$

$\longrightarrow \: \boxed {\mathfrak{ {y}^{2} = 100}}$

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