Question

The Euler form of $\frac{2+6\sqrt{3}i}{5+i\sqrt{3}}$ is

• A. $2\cdot e^{i\frac{\pi }{6}}$
• B. $e^{i\pi /3}$
• C. $e^{-2\pi /3}$
• D. $2e^{i\frac{\pi }{3}}$

Answer 1

Answer: (D)

Let $z=\frac{2+6\sqrt{3}i}{5+i\sqrt{3}}$
$=\frac{(2+6\sqrt{3}i)(5-i\sqrt{3})}{28}$
$=2\left(\frac{1+i\sqrt{3}}{2}\right)=2\left(cos\frac{\pi }{3}+isin\frac{\pi }{3}\right)=2e^{i\pi /3}$