From theory to practice

a historical analysis of the conceptual development of complex numbers and their application

Abstract

The work analyses the historical evolution of the concept of complex numbers, since when they were first needed in the mathematical context until their eventual formalization and acceptance. The main analysis comprises the Middle Ages, that is, the beginning of European Renaissance and the transition from feudalism to capitalism, a fruitful cultural period that influenced Philosophy, Arts and Sciences as well as Mathematics. The article will make a “journey” since the Sumerians’ clay tablets, some 3.700 years ago, until the fractal generators of the present time, showing the mathematicians’ reserve in accepting them, as it had occurred with negative numbers. Today the theory of complex numbers is applied in technology, sciences, arts and nature.