On moduli and arguments of roots of complex trinomials

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dc.contributor.authorČermák, Jancs
dc.contributor.authorFedorková, Luciecs
dc.contributor.authorJánský, Jiřícs
dc.coverage.issue1cs
dc.coverage.volume332cs
dc.date.accessioned2025-04-08T13:56:13Z
dc.date.available2025-04-08T13:56:13Z
dc.date.issued2024-11-20cs
dc.description.abstractRoot properties of a general complex trinomial have been explored in numerous papers. Two questions have attracted a significant attention: the relationships between the moduli of these roots and the trinomial’s entries, and the location of the roots in the complex plane. We consider several particular problems connected with these topics, and provide new insights into them. As two main results, we describe the set of all trinomials having a root with a given modulus, and derive explicit formula for calculations of the arguments of such roots. In this fashion, we obtain a comprehensive characterization of these roots. In addition, we develop a procedure enabling us to compute moduli and arguments of all roots of a general complex trinomial with arbitrary precision. This procedure is based on the derivation of a family of real transcendental equations for the roots’ moduli, and it is supported by the formula for their arguments. All our findings are compared with the existing results.en
dc.formattextcs
dc.format.extent39-67cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationPACIFIC JOURNAL OF MATHEMATICS. 2024, vol. 332, issue 1, p. 39-67.en
dc.identifier.doi10.2140/pjm.2024.332.39cs
dc.identifier.issn0030-8730cs
dc.identifier.orcid0000-0002-6884-917Xcs
dc.identifier.other191359cs
dc.identifier.researcheridD-2542-2014cs
dc.identifier.urihttps://hdl.handle.net/11012/250860
dc.language.isoencs
dc.publisherMathematical Sciences Publisherscs
dc.relation.ispartofPACIFIC JOURNAL OF MATHEMATICScs
dc.relation.urihttps://msp.org/pjm/2024/332-1/pjm-v332-n1-p03-p.pdfcs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/0030-8730/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectComplex trinomialen
dc.subjectrooten
dc.subjectlocationen
dc.subjectmodulusen
dc.subjectargumenten
dc.titleOn moduli and arguments of roots of complex trinomialsen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-191359en
sync.item.dbtypeVAVen
sync.item.insts2025.04.08 15:56:13en
sync.item.modts2025.04.08 15:33:01en
thesis.grantorVysoké učení technické v Brně. Fakulta strojního inženýrství. Ústav matematikycs
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