1. Tardigrade
  2. Question
  3. Mathematics
  4. The value of |√2i-√-2i| is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

Complex Numbers and Quadratic Equations

Solution:

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