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Finding the imaginary part

Poly

Member
Nov 26, 2012
32
How do I find the imaginary part of $\displaystyle \frac{1}{i}xe^{-ix}+e^{ix}$?
 
Last edited:

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
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:

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

Poly

Member
Nov 26, 2012
32
Sorry there was an $i$ missing from the first part. But I got the answer using your suggestion. Thanks.