Question

The modulus of the complex number $z=\frac{1-i}{3-4i}$ is

• A. $\frac{5}{\sqrt{2}}$
• B. $\frac{\sqrt{2}}{5}$
• C. $\sqrt{\frac{2}{5}}$
• D. none of these

Answer 1

Answer: (B)

$\frac{\sqrt{2}}{5}$

Now,

$z=\frac{1-i}{3-4i}$

or, $z=\frac{(1-i)(3+4i)}{3^2+4^2}$

or, $z=\frac{7+i}{25}$.

Then $|z|=\sqrt{{\left(\frac{7}{25}\right)}^2+{\left(\frac{1}{25}\right)}^2}=\frac{\sqrt{50}}{25}=\frac{\sqrt{2}}{5}$.