Some useful values of the complex exponential to know by heart are $e^{2{\rm i } \pi} = 1 $, $e^{{\rm i} \pi} = -1 $ and $e^{{\rm i} \pi/2} = {\rm i}$.
From the first expression, it also follows that
$$e^{{\rm i} (y + 2\pi n)} = e^{{\rm i}\pi} {\rm ~ for ~} n \in \mathbb{Z}$$
$$e^{{\rm i} (y + 2\pi n)} = e^{{\rm i}y} {\rm ~ for ~} n \in \mathbb{Z}$$
As a result, $y$ is only defined up to $2\pi$.
Furthermore, we can define the sine and cosine in terms of complex exponentials:
