Question

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

• A. 15
• B. 25
• C. -25
• D. None of these

Answer 1

The correct option is B

25

$\sqrt{-7-24i}$=x-iy

Squaring both sides, -7-24i=$x^2$-$y^2$-i(2xy)

Equating real and imaginary parts,we get

$x^2$-$y^2$=-7 And 2xy=24

$\therefore$ $x^2$+$y^2$= $\sqrt{49+576}$=$\sqrt{625}$=25