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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Authors: 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
Format: article
Publication Date:2025
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/230151
Online Access:https://riunet.upv.es/handle/10251/230151
Access Level:Open access
Keyword:Complex variable
Complex exponential
Complex logarithm
Complex power of a complex number
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spelling The Exponential Versus the Complex Power ez Function RevisitedSánchez Ruiz, Luis Manuel|||0000-0001-7559-6724Moll López, Santiago Emmanuel|||0000-0003-3388-5135Moraño Fernández, José Antonio|||0000-0003-4385-7277Roselló, María-Dolores|||0000-0002-5724-7683Legua, MatildeComplex variableComplex exponentialComplex logarithmComplex power of a complex number[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.MDPI AGDepartamento de Matemática AplicadaEscuela Técnica Superior de Ingeniería Aeroespacial y Diseño IndustrialInstituto Universitario de Matemática MultidisciplinarCentro de Investigación en Tecnologías GráficasRepositorio Institucional de la Universitat Politècnica de València Riunet20252025-04-16journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/230151reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2301512026-06-13T07:49:27Z
dc.title.none.fl_str_mv The Exponential Versus the Complex Power ez Function Revisited
title The Exponential Versus the Complex Power ez Function Revisited
spellingShingle The Exponential Versus the Complex Power ez Function Revisited
Sánchez Ruiz, Luis Manuel|||0000-0001-7559-6724
Complex variable
Complex exponential
Complex logarithm
Complex power of a complex number
title_short The Exponential Versus the Complex Power ez Function Revisited
title_full The Exponential Versus the Complex Power ez Function Revisited
title_fullStr The Exponential Versus the Complex Power ez Function Revisited
title_full_unstemmed The Exponential Versus the Complex Power ez Function Revisited
title_sort The Exponential Versus the Complex Power ez Function Revisited
dc.creator.none.fl_str_mv 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
author Sánchez Ruiz, Luis Manuel|||0000-0001-7559-6724
author_facet 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
author_role author
author2 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
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial
Instituto Universitario de Matemática Multidisciplinar
Centro de Investigación en Tecnologías Gráficas
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Complex variable
Complex exponential
Complex logarithm
Complex power of a complex number
topic Complex variable
Complex exponential
Complex logarithm
Complex power of a complex number
description [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.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-04-16
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/230151
url https://riunet.upv.es/handle/10251/230151
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv MDPI AG
publisher.none.fl_str_mv MDPI AG
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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