The Exponential Versus the Complex Power ez Function Revisited

[EN] The complex exponential function exp is a well-known entire function. In this paper, we recall its relation with the definition of the complex power of a complex number, which emanates that the complex power ez may coincide with it at some complex values. Still, on most occasions, the power rep...

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Detalles Bibliográficos
Autores: Sánchez Ruiz, Luis Manuel|||0000-0001-7559-6724, Moll López, Santiago Emmanuel|||0000-0003-3388-5135, Moraño Fernández, José Antonio|||0000-0003-4385-7277, Roselló, María-Dolores|||0000-0002-5724-7683, Legua, Matilde
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/230151
Acceso en línea:https://riunet.upv.es/handle/10251/230151
Access Level:acceso abierto
Palabra clave:Complex variable
Complex exponential
Complex logarithm
Complex power of a complex number
Descripción
Sumario:[EN] The complex exponential function exp is a well-known entire function. In this paper, we recall its relation with the definition of the complex power of a complex number, which emanates that the complex power ez may coincide with it at some complex values. Still, on most occasions, the power represents a much broader spectrum of complex values. We also outsight how the software Mathematica may become a valuable tool for evaluating and visualizing complex power functions, in some cases by introducing some specific commands that have not been implemented in the software.