Question

Find the modulus of the complex number, $\sqrt{2}i+\sqrt{-2}i$.

Answer 1

$\sqrt{2}i+\sqrt{2}i$

$=\sqrt{2}i+\sqrt{-1}\times \sqrt{2}\times i$

$=\sqrt{2}i+i\times \sqrt{2}\times i$

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

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

Modulus is $\sqrt{2}\cdot \sqrt{(-1{)}^2+i^2}=\sqrt{2}\cdot \sqrt{2}=2$.