If is a nonzero complex numbers and let
where
- Compute , , and .
- Prove that if , and are in with .
- What conditions on and must we have for the equation
to hold? Show that the equation fails when and .
- The computations are as follows,
- Proof. Using the definitions we compute,
- First, if and then we have
but
Thus,
In order for we must have since
and only when .
There is a typo in the line before the last one: exp(2ni \pi) should be exp(2niw \pi).
This question, as formulated in Apostol, is wrong. See: http://scipp.ucsc.edu/~haber/ph116A/clog_11.pdf
(Great work in this site!)
Mind explaining what’s wrong? you claim that Apostol is wrong without explanation and give a link to 14 pages with “physics 116A” on the first page