Group structure of unity of roots

Lanwen Zhang; Zhihao Zou

doi:10.1117/12.2628167

22 April 2022 Group structure of unity of roots

Lanwen Zhang, Zhihao Zou

Proceedings Volume 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021); 121634C (2022) https://doi.org/10.1117/12.2628167
Event: International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 2021, Nanjing, China

Abstract

The theory of complex functions deals with calculus over complex variables. In this paper, we review the knowledge about complex numbers systematically from a higher vision. Algebraically, the set of all complex numbers forms a field. Geometrically, all complex numbers form a complete metric space, which owns an elegant topological structure. Mathematicians deal with technical problems using complex numbers in a very concise way. We summarize the computational and algebraic properties of complex numbers and discuss their geometric representation. Then, we discuss the group structure of unity of roots in detail and give detailed proofs of several elegant results.

Citation Download Citation

Lanwen Zhang and Zhihao Zou "Group structure of unity of roots", Proc. SPIE 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 121634C (22 April 2022); https://doi.org/10.1117/12.2628167

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