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  4. If √-7-24 i=x+i y, then find x2+y2

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Q. If $\sqrt{-7-24 i}=x+i y$, then find $x^{2}+y^{2}$

Complex Numbers and Quadratic Equations

Solution:

$x+i y=\sqrt{-7-24 i}$
$\Rightarrow x-i y=\sqrt{-7-24 i}$
$\ldots$ [Writing complex conjugate]
$\Rightarrow x^{2}+y^{2}=(x+i y)(x-i y)$
$=\sqrt{(-7+24 i)(-7-24 i)}$
$=\sqrt{49+576}$
$=\sqrt{625}=25$