What is the modulus of `(sqrt2+i)/(sqrt2-i)where i =sqrt(-1)`?

Options

A. 3
B. 43467
C. 1
D. None of the above

Answer

C

Explanation

Let `z=(sqrt2+i)/(sqrt2-i)=(sqrt2+i)/(sqrt-i)xx(sqrt2+i)/(sqrt2+i)`
`=((sqrt2+i)^(2))/((sqrt2)^(2)-(i)^(2))=(2sqrt2i+1)/(3)`
`impliesz=(2sqrt2)/(3)i+1/3`
Now, `|z|=sqrt(((2sqrt2)/(3))^(2)+((1)/(3))^(2))=1`