Publication detail
On moduli and arguments of roots of complex trinomials
ČERMÁK, J. FEDORKOVÁ, L. JÁNSKÝ, J.
English title
On moduli and arguments of roots of complex trinomials
Type
journal article in Web of Science
Language
en
Original abstract
Root 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.
English abstract
Root 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.
Keywords in English
Complex trinomial, root, location, modulus, argument
Released
20.11.2024
Publisher
Mathematical Sciences Publishers
Location
Los Angeles, , USA
ISSN
0030-8730
Volume
332
Number
1
Pages from–to
39–67
Pages count
29
BIBTEX
@article{BUT191359,
author="Jan {Čermák} and Lucie {Fedorková} and Jiří {Jánský},
title="On moduli and arguments of roots of complex trinomials",
year="2024",
volume="332",
number="1",
month="November",
pages="39--67",
publisher="Mathematical Sciences Publishers",
address="Los Angeles, , USA",
issn="0030-8730"
}