Question

Express the following complex number in the polar form
$\frac{2+6\sqrt{3}i}{5+\sqrt{3}i}$

Answer 1

$\frac{2+6\sqrt{3}i}{5+\sqrt{3}i}\frac{5-\sqrt{3}i}{5-\sqrt{3}i}=\frac{10-2\sqrt{3}i+30\sqrt{3}i+18}{25+3}$

$=\frac{28+28\sqrt{3}i}{28}=1+\sqrt{3}i=2(\frac{1}{2}+\frac{\sqrt{3}}{2}i)$

$=2(cos{60}^{\circ }+isin{60}^{\circ })=2cis{60}^{\circ }$