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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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-04-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/8/1306 |
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| Summary: | 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. |
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| ISSN: | 2227-7390 |