Mapping of a Complex Variable with a Unimodular Quadratic Function where all the Coefficients of the Quadratic are Unity versus Mapping of a Quadratic Function of a Unimodular Complex Variable where all the Coefficients of the Quadratic are Unity

Abstract

In this paper an attempt has been made to find out the mapping pattern of a complex variable z with a unimodular quadratic function f(z), where all the coefficients of the quadratic are unity. Applying this concept one can conclude the solution set of all possible z or can determine the locus of z on Argand Plane, when f(z) lies on a unit circle whose center is at origin. Also attempted to find out the mapping pattern of a quadratic function f(z) of a unimodular complex variable z, where all the coefficients of the quadratic are unity. Applying this concept one can conclude the solution set of all possible f(z) or can determine the locus of f(z) on Argand Plane, when z lies on a unit circle whose center is at origin.