Question

The modulus of the complex number $z=\frac{\left(1-i\sqrt{3}\right)\left(cos\theta +isin\theta \right)}{2\left(1-i\right)\left(cos\theta -isin\theta \right)}$ is

• A. $\frac{1}{2\sqrt{2}}$
• B. $\frac{1}{\sqrt{3}}$
• C. $\frac{1}{\sqrt{2}}$
• D. $2\sqrt{3}$

Answer 1

Answer: (C)

$\left|cos\theta +isin\theta \right|=\left|cos\theta -isin\theta \right|=1$
$\therefore \left|z\right|=\frac{|1-i\sqrt{3}|}{2|1-i|}$
$=\frac{2}{2\sqrt{2}}$
$=\frac{1}{\sqrt{2}}$