Question

The value of $\left|\sqrt{2i}-\sqrt{-2i}\right|$ is

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

Answer 1

Answer: (A)

$\sqrt{2i}-\sqrt{-2i}=\sqrt{{\left(1+i\right)}^2}-\sqrt{{\left(1-i\right)}^2}$
$=\left(1+i\right)-\left(1-i\right)=2i$
$\therefore \left|\sqrt{2i}-\sqrt{-2i}\right|=\left|2i\right|=\sqrt{0+4}$
$=2$