Question

Find square root of $-7-24i$.

• A. $\pm (3+4i).$
• B. $\pm (3-4i).$
• C. $\pm (4-3i).$
• D. $\pm (4+3i).$

Answer 1

The correct option is B $\pm (3-4i).$

Let square root of $-7-24i$ is $z$
$\Rightarrow z^2=-7-24i=-7-2\cdot 3\cdot 4i$
$\Rightarrow z^2=-16+9-2\cdot 3\cdot 4i$
$\Rightarrow z^2=16i^2+9-2\cdot 3\cdot 4i=(-4i{)}^2-2\cdot 3\cdot 4i+(3{)}^2$
$\Rightarrow z^2=(3-4i{)}^2,[\because (a-b{)}^2=a^2-2ab+b^2]$
$\therefore z=\pm (3-4i)$