Complex Integration from a List

① This GeoGebra example demonstrates how to construct a complex integration path from a given list of complex points and compute the integral of a complex function along that path, showing how the integral value changes with the path and function. ② Core mathematical concepts include complex line integrals, parametric curves, Riemann sum approximation, and path integration in the complex plane, involving summation of function values at discrete sample points multiplied by infinitesimal displacements. ③ Construction highlights: using commands such as Sequence, Zip, Element, Vector, CurveCartesian, Sphere, Intersect, Segment, Textfield, and Integral to generate complex lists, function value sequences, path vectors, parametric curves, and to compute real and imaginary parts of the integral; interactive sliders and text fields allow adjusting parameters like n, a, b, dt. ④ Suitable for university-level complex analysis courses in mathematics or physics, and for instructors demonstrating path independence, Cauchy's integral theorem, or the effect of singularities on integrals, helping students visualize the relationship between integration paths and function behavior.