Question

Represent the following complex number in trigonometric form:
$\frac{3}{2}-i\frac{\sqrt{3}}{2}$

Answer 1

$\frac{3}{2}$$-i\frac{\sqrt{3}}{2}=r{e}^{i\theta }$

$r=\sqrt{\frac{9}{4}+\frac{3}{4}}=\sqrt{3}$

$\theta ={\tan }^{-1}(-\frac{\sqrt{3}}{2}\times \frac{2}{3})=\frac{-\pi }{6}$

$⟹\sqrt{3}{e}^{-i\pi /6}$