/sci/ - Science & Math

Hi /sci

I was doing some differential equations in my own with help of complex numbers and came up with this formula
<span class="math">e^{ix}ln(e^{ix}+e^{-ix})+e^{-ix}ln(e^{-ix}+e^{ix})[/spoiler]


and it appears to be sum of number <span class="math">e^{ix}ln(e^{ix}+e^{-ix})[/spoiler]
and its complex conjugate, so their sum should be real. But


http://www.wolframalpha.com/input/?i=e^%28ix%29ln%28e^%28ix%29%2Be^%28-ix%29%29%2Be^%28-ix%29ln%28e^%28-ix%29%2Be^%28ix%29%29


says it has an imaginary part. How is this possible?
Thanks in advance.

Is it true that nothing in nature happens definitively unless there's a human there to observe the event or its aftermath?