Question

If $(-7-24i{)}^{1/2}=x-iy$, then $x^2+y^2=$

• A. 15
• B. 25
• C. $-25$
• D. $-15$

Answer 1

Answer: (B)

$z=(-7-24i{)}^{1/2}$
$z^2=-7-24i$
$z=x-iy$
$z^2=x^2-y^2-2ixy$
$x^2-y^2=-7$
$2xy=24$
$xy=12$
${\left(x^2-y^2\right)}^2+4x^2{y}^2={\left(x^2+y^2\right)}^2$
$49+4.144={\left(x^2+y^2\right)}^2$
${\left(x^2+y^2\right)}^2=25^2$
$x^2+y^2=25$