Question

The modulus of $\sqrt{2i}-\sqrt{-2i}$ is

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

Answer 1

The correct option is A $2$

$|\sqrt{2i}-\sqrt{-2i}|$

$\Rightarrow \sqrt{(\sqrt{2i}-\sqrt{-2i})(\sqrt{2i}-\sqrt{-2i})}$

$\Rightarrow \sqrt{2i-2i-2\sqrt{2i\times -2i}}$

$\Rightarrow \sqrt{0-2}\sqrt{4\left(1\right)}$

$\Rightarrow \sqrt{2\left(2\right)}\Rightarrow 2$