The study of cases of fixed points of a complex function depending on the inputs and concluding examples of useful functions

Abstract This is a mathematical article that deals with the domain of complex numbers in order to present new results by using a complex function and studying its fixed points. The aim of this work is to propose mathematical procedures that help to deduce the fixed points of a complex function. These fixed points can also be used as a basis to generate new useful complex functions that have for sure at least one fixed point. Hence, this is a good article to be read by specialists of Calculus and Analysis and even by the beginners of mathematics who want to improve their skills in the field of complex numbers.