Question

Find the modulus of the complex number $\frac{1+i}{3-i}$.

Answer 1

Let $z$ be the complex number.

Then according to the problem we've,

$z=$ $\frac{1+i}{3-i}$

or, $z=$ $\frac{(1+i)(3+i)}{3^2-i^2}$

or, $z=$ $\frac{2+4i}{10}$

or, $z=$ $\frac{1+2i}{5}$.

Now, $|z|=\frac{1}{5}\times \sqrt{1^2+2^2}=\frac{1}{\sqrt{5}}$.