Question

Represent $1+\cos \frac{\pi }{3}+i\sin \frac{\pi }{3}$ in polar form.

Answer 1

$1+\cos \frac{\pi }{3}+i\sin \frac{\pi }{3}$

$=2{\cos }^2\frac{\pi }{6}+i.2\sin \frac{\pi }{6}\cos \frac{\pi }{6}$

$=2\cos \frac{\pi }{6}(\cos \frac{\pi }{6}+i\sin \frac{\pi }{6})$

$=2\cos \frac{\pi }{6}{e}^{\frac{i\pi }{6}}$