We all know from ordinary calculus that an simple integral means to sum up a lot of pieces of area, double integrals a lot of pieces of volume, and so on (roughly speaking, of course).
I'm now studying line integrals on the complex plane, and i want to know if there is some kind of 'meaning' on them. I know what i am summing up, but i don't understand what the result means, for a finite line. Does the final result has a meaning? For example, if a line integral along a curve $C$ equals $z=a+bi$, what is the meaning of $z$?(if there is a meaning at all). Thanks.