The error functions in the complex plane, their properties and implications

In this scientific study, various and necessary information directly related to the familiar error functions, which are in the family of classical special functions and are important tools for almost all-natural sciences and technology, and are considered in some regions of the complex plane, will firstly be introduced. Several main results involving various analytical and geometric properties of error functions, generated with the help of some auxiliary theorems used in recent studies, will then be determined (and then proven). A number of implications of the relevant main results and some possible specific applications will also be highlighted for interested researchers.