Question

write in polar form 2+6√3i/5+√3i​

Answer 1

Answer:

2∠π/3

Step-by-step explanation:

$\frac{2 + 6 \sqrt{3} i}{5 + \sqrt{3} i} \\ = \frac{2 + 6 \sqrt{3} i}{5 + \sqrt{3} i} \times \frac{5 - \sqrt{3} i}{5 - \sqrt{3} i}$

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

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

Amplitude A is

$\sqrt{ {1}^{2} + { \sqrt{3} }^{2} } = 2$

Angle is

$tan \: inverse ( \frac{ \sqrt{3} }{1} ) = \frac{\pi}{3}$