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  4. The modulus of ((1+i√3)(2+2i)/(√3-i)) is

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

Complex Numbers and Quadratic Equations

Solution:

$\left|\frac{\left(1+i\sqrt{3}\right)\left(2+2i\right)}{\sqrt{3}-i}\right|=\frac{\left|1+i\sqrt{3}\right|\left|2+2i\right|}{\left|\sqrt{3}-i\right|}$
$=\frac{2\times2\sqrt{2}}{2}=2\sqrt{2}$