Question

The square root of $(7-24i)$ is

• A. $\pm (3-5i)$
• B. $\pm (3+4i)$
• C. $\pm (3-4i)$
• D. $\pm (4-3i)$

Answer 1

Answer: (D)

Let $z=7-24i=7-2\cdot 4\cdot 3i=16-9-2\cdot 4\cdot 3i$
$=(4{)}^2+(-3i{)}^2-2\cdot 4\cdot 3i=(4-3i{)}^2$
$\therefore \sqrt{7-24i}=\pm (4-3i)$