I am given an expression like this:
$$\int_0^1 e^{-2\pi int} f(t) dt$$
How can I evaluate this, just give me glance,like some line how to treat that i,I don't want actual solution.
2026-03-29 16:01:20.1774800080
Evaluating a class of complex integrals
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This is a discrete Fourier transform. It's not something you solve in this general form (that can't really be done). You solve it separately for each and every $f$ you encounter. Some $f$s make it easy, some make it hard, and some make it impossible.
As for what to do with $i$, you treat it like any other constant, because that's what it is. It happens to be a constant such that $i^2 = -1$, and it happens to interact nicely with the exponential function, but at the end of the day, it's just a constant like any other.