What is the most correct way to write the polar form of a complex number?
For example, given the complex number: $\dfrac{\sqrt{3}}{2} + \dfrac{1}{2}i$ I would write the polar form as follows:
\begin{align} \dfrac{\sqrt{3}}{2} + \frac 12 i &= \cos\left(\frac{\pi}{6}\right)+i\sin\left(\frac{\pi}{6}\right) \\ &= e^{i{\pi}/{6}} \end{align}
My question is what about every other integer multiple of $2\pi$? Should I write this as: $e^{i\pi/{6} + 2\pi k}$ for $k\in\mathbb{N}$
Thanks for the help!