Except that e^(j*pi) = -1.  Look up Eueler's identity/Euler's formula.
(yes, j, not i...real engineers know that i is time-domain current!)
The summation is correct.  It does work out to 1.
Therefore, this check is made out for 0.002 - 1 + 1 = 0.002.  I presume this is in reference to the "0.002 cents per kilobyte" fiasco.
Just my 0.002 cents...
Oh, and FWIW, engineering does frequently use the e^(j*stuff) thing as it is a common way to represent complex numbers in "polar" format.  The EEs use this all the time, but they'd use j, not i, so I have no idea what's up with that check.  The other engineering disciplines (that would be more apt to use i for sqrt(-1)) tend to have less use for that sort of thing.