Question

The value of $\sqrt{8-6i}$ is

• A. $\pm (3-4i)$
• B. $\pm (3-2i)$
• C. $\pm (3-i)$
• D. $\pm (3+4i)$

Answer 1

The correct option is C $\pm (3-i)$

Using square root formula, we have
$\sqrt{a-ib}=\pm (\sqrt{\frac{\sqrt{(a^2+b^2)}+a}{2}}-i\sqrt{\frac{\sqrt{(a^2+b^2)}-a}{2}})$
If $b>0$
$a=8,b=6$

Hence,
$\sqrt{8-6i}=\pm (\sqrt{\frac{10+8}{2}}-i\sqrt{\frac{10-8}{2}})=\pm (3-i)$