Let's say you integrate a complex function along a curve. How do you visualize it? This is explaned very well in multivariate calculus in terms of work, or for instance the weight of the line of we integrate over the density etc.. But when we look at complex function I get this: The function F is a complex number, and then we multiply it with dz, this means that what we are doing informally is adding the product of complex numbers. But if we multiply complex number we take one of them, and rotate it with the angle of the other one, and scale its absolute value(its new absolute value is the product of both absolute values). Now I can not make sense of this. Can you? How do you informally look at a complex line integral?