Question

The modulus of $\frac{\left(1+i\sqrt{3}\right)\left(2+2i\right)}{\left(\sqrt{3}-i\right)}$ is

• A. $2$
• B. $4$
• C. $3\sqrt{2}$
• D. $2\sqrt{2}$

Answer 1

Answer: (D)

$\left|\frac{\left(1+i\sqrt{3}\right)\left(2+2i\right)}{\sqrt{3}-i}\right|=\frac{|1+i\sqrt{3}||2+2i|}{|\sqrt{3}-i|}$
$=\frac{2\times 2\sqrt{2}}{2}=2\sqrt{2}$