How to write $e^{\pi+i}$ as $a+bi$

Question

How can I find the $a+bi$ form of the number $e^{\pi+i}$? Normally, it is $e^{i \pi} = \cos(\pi) + i \sin(\pi)$ but in this case, I don't find any clue.

Answer 1

$$e^{\pi+i}=e^\pi\times e^i=e^\pi(\cos{(1)}+i\sin{(1)})=e^\pi\cos{(1)}+e^\pi\sin{(1)}i$$