Question

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

Answer 1

Answer: 25

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