Question

Why does this integral come out imaginary?

Answer 1

Answer:

The basic theme here is that complex line integrals will mirror much of what we've seen for ... More precisely, if f(z) is defined on a region A then. ∫ ... Likewise for the imaginary piece: ∫

Answer 2

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if you mean complex valued function of a real variable, you can integrate the real and imaginary parts separately. But there may be no need to do so. For example the integral of is just as for real functions. The case of a function of a real variable is a special case, you are just integrating along the real axis.