Polar Form of Complex Number/Examples/2 + 2 root 3 i

Example of Polar Form of Complex Number
The complex number $2 + 2 \sqrt 3 i$ can be expressed as a complex number in polar form as $\polar {4, \dfrac \pi 3}$.

Proof

 * 2 + 2 root 3 i.png

Then:

Hence:
 * $\map \arg {2 + 2 \sqrt 3 i} = \dfrac \pi 3$

and hence the result.