, where i is the imaginary unit and n is an entire.
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Compute and take the imaginary part.
Originally Posted by girdav Compute and take the imaginary part. has a real part and a imaginary part, while if i take the imaginary part of i'll have no real part. Is that correct?
Originally Posted by girdav Compute and take the imaginary part. Actually this doesn't work. Consider briefly that it will return a real answer, which is obviously not correct.
I'd do it by parts. Here's the first step:
Do the second integral by parts and you will have the form:
from which you can solve for .
Unless I am misreading something I dont think this is purely real.
You could also use
Last edited by TheEmptySet; June 6th 2011 at 04:37 PM.
Originally Posted by girdav Compute and take the imaginary part. The title of the original question is misleading. The above method works for , but not for the posted question, viz. .
If we don't want to do it by parts, we can write as . Now we have to compute and .
For the first we use and for the second .
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