17 - Curves in the Complex Plane

Suppose that we have two points , mapped to the complex plane by a function , with

Image(trace)

The of the curve is the set of every point mapped by the function, basically just like the image in real numbers.

Differentiability

The curve(function) is of class , n-times differentiable if both are also n-times differentiable(of class )

Piecewise Differentiability

The function is piecewise differentiable if there exist combinations of so that it's also differentiable on that interval.