MHB Imaginary Part of a Complex Function: How to Find It?

[Poly1]

How do I find the imaginary part of $\displaystyle \frac{1}{i}xe^{-ix}+e^{ix}$?

 

[MarkFL]

For the first term, I would rewrite i with a negative exponent, then apply:

$\displaystyle i^{n}=i^{n+4k}$ where $\displaystyle k\in\mathbb{Z}$

For the second term, apply Euler's formula:

$\displaystyle e^{\theta i}=\cos(\theta)+i\sin(\theta)$

 

[Poly1]

Sorry there was an $i$ missing from the first part. But I got the answer using your suggestion. Thanks.