Question

The square root of $\left(-5-12i\right)$ is

• A. $\pm \left(3+2i\right)$
• B. $\pm \left(2+3i\right)$
• C. $\pm \left(2-3i\right)$
• D. $\pm \left(3-2i\right)$

Answer 1

Answer: (C)

Let $z=-5-12i$
$=-5-2\left(6i\right)$
$=-9+4-2\cdot 2\left(3i\right)$
$={\left(-3i\right)}^2+2^2+2\cdot 2\left(-3i\right)$
$\therefore z=-5-12i$
$={\left(2-3i\right)}^2$
$\therefore \sqrt{-5-12i}=\pm \left(2-3i\right)$