Question

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

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