TITLE: What is $\Re(e^i)$?
QUESTION [5 upvotes]: What is $\Re(e^i)$?

My book says answer is $e$.  Can that be right?
I know $e^{i \pi} = \cos \pi + i \sin \pi = -1$
So that would mean $e^i = \cos 1 + i \sin 1$ and the real part would be $\cos 1$.  That's not the book's answer.

REPLY [7 votes]: You're right, $e^i=\cos 1+i \sin 1$. So the answer is $\cos 1$.