Amplitwist


In mathematics, the amplitwist is a concept created by Tristan Needham in the book Visual Complex Analysis to represent the derivative of a complex function visually.

Definition

The amplitwist associated with a given function is its derivative in the complex plane. More formally, it is a complex number such that in an infinitesimally small neighborhood of a point in the complex plane, for an infinitesimally small vector. The complex number is defined to be the derivative of at.

Uses

The concept of an amplitwist is used primarily in complex analysis to offer a way of visualizing the derivative of a complex-valued function as a local amplification and twist of vectors at a point in the complex plane.

Examples

Define the function. Consider the derivative of the function at the point. Since the derivative of is, we can say that for an infinitesimal vector at,.