Question

What is the modulus of $\frac{\sqrt{2}+i}{\sqrt{2}-i}$ where $i=\sqrt{-1}$

• A. $3$
• B. $\frac{1}{2}$
• C. $1$
• D. None of the above

Answer 1

The correct option is C $1$

$\left|\frac{\sqrt{2}+i}{\sqrt{2}-i}\right|=\frac{\sqrt{(\sqrt{2}{)}^2+1^2}}{\sqrt{(\sqrt{2}{)}^2+(-1{)}^2}}=1$
Hence, option C is correct.