The Exponential Versus the Complex Power <i>e<sup>z</sup></i> Function Revisited
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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display=...
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2025-04-01
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| author | Luis M. Sánchez-Ruiz Matilde Legua Santiago Moll-López José A. Moraño-Fernández María-Dolores Roselló |
| author_facet | Luis M. Sánchez-Ruiz Matilde Legua Santiago Moll-López José A. Moraño-Fernández María-Dolores Roselló |
| author_sort | Luis M. Sánchez-Ruiz |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>e</mi><mi>z</mi></msup></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>e</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>a</mi></mrow></semantics></math></inline-formula> 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. |
| format | Article |
| id | doaj-art-3b6479c4a63e4e43a73da108a8afd1e5 |
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| issn | 2227-7390 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
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| spelling | doaj-art-3b6479c4a63e4e43a73da108a8afd1e52025-08-20T03:13:58ZengMDPI AGMathematics2227-73902025-04-01138130610.3390/math13081306The Exponential Versus the Complex Power <i>e<sup>z</sup></i> Function RevisitedLuis M. Sánchez-Ruiz0Matilde Legua1Santiago Moll-López2José A. Moraño-Fernández3María-Dolores Roselló4Departamento de Matemática Aplicada, Universitat Politècnica de València, 46022 Valencia, SpainDepartmento de Matemática Aplicada, Universidad de Zaragoza, 50018 Zaragoza, SpainDepartamento de Matemática Aplicada, Universitat Politècnica de València, 46022 Valencia, SpainDepartamento de Matemática Aplicada, Universitat Politècnica de València, 46022 Valencia, SpainDepartamento de Matemática Aplicada, Universitat Politècnica de València, 46022 Valencia, SpainThe 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>e</mi><mi>z</mi></msup></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>e</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>a</mi></mrow></semantics></math></inline-formula> 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.https://www.mdpi.com/2227-7390/13/8/1306complex variablecomplex exponentialcomplex logarithmcomplex power of a complex number |
| spellingShingle | Luis M. Sánchez-Ruiz Matilde Legua Santiago Moll-López José A. Moraño-Fernández María-Dolores Roselló The Exponential Versus the Complex Power <i>e<sup>z</sup></i> Function Revisited Mathematics complex variable complex exponential complex logarithm complex power of a complex number |
| title | The Exponential Versus the Complex Power <i>e<sup>z</sup></i> Function Revisited |
| title_full | The Exponential Versus the Complex Power <i>e<sup>z</sup></i> Function Revisited |
| title_fullStr | The Exponential Versus the Complex Power <i>e<sup>z</sup></i> Function Revisited |
| title_full_unstemmed | The Exponential Versus the Complex Power <i>e<sup>z</sup></i> Function Revisited |
| title_short | The Exponential Versus the Complex Power <i>e<sup>z</sup></i> Function Revisited |
| title_sort | exponential versus the complex power i e sup z sup i function revisited |
| topic | complex variable complex exponential complex logarithm complex power of a complex number |
| url | https://www.mdpi.com/2227-7390/13/8/1306 |
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