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)

$\pm \left(2-3i\right)$

Answer 2

Let $z=-5-12i$ $=-5-2\left(6i\right)$ $=-9+4-2\cdot2\left(3i\right)$ $=\left(-3i\right)^{2}+2^{2}+2\cdot2\left(-3i\right)$ $\therefore\, z=-5-12i$ $=\left(2-3i\right)^{2}$ $\therefore\, \sqrt{-5-12i}=\pm\left(2-3i\right)$