Question

A value of $\sqrt{i}+\sqrt{-i}$ is

• A. 0
• B. $\sqrt{2}$
• C. $-i$
• D. $i$

Answer 1

Answer: (B)

$\sqrt{i}+\sqrt{-i}=\frac{1}{\sqrt{2}}(\sqrt{2i}+\sqrt{-2i})$
$=\frac{1}{2}\{\sqrt{{(1+i)}^2}+\sqrt{{(1-i)}^2}\}$
$=\frac{1}{\sqrt{2}}\{(1+i)+(1+i)\}$
$=\sqrt{2}$