The Recursive Phase Generator Theorem: How the Sq root of đť‘– Constructs the Complex Unit Circle
Year: 2025
Type: article
Abstract: This paper introduces and proves the Recursive Phase Generator Theorem, which establishes ithe Square root of i as the minimal recursive generator of complex phase space. Grounded in Euler’s identity, De Moivre’s theorem, and classical group theory, the proof demonstrates that i\sqrt{i}i alone generates all 8th roots of unity through recursive multiplication, constructing the full discrete symmetry of the complex unit circle. This result reveals a deep connection between recursion, emergence, and symmetry-breaking embedded within the complex plane itself. The work reframes i\sqrt{i}i not as a derived quantity, but as a foundational algebraic and geometric operator—central to both mathematical structure and potential physical interpretation.
Author: Thavarajah, Rogan
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6931116088
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