Abstract We introduce a novel reinterpretation of classical trigonometric functions within the framework of extended complex numbers, denoted as Cn-numbers (Aktas numbers). Unlike the conventional view where sine and cosine behave as single pure oscillators, we demonstrate that their series expansions naturally decompose into layered carrier modes. Each term of the Taylor expansion is identified as a distinct “phase carrier,” representing hidden structural layers of the wavefunction. This decomposition suggests that the apparent simplicity of sinusoidal functions masks a multi-carrier architecture with direct implications for quantum mechanics. In particular, the proposed carrier-based formalism provides a new pathway for modeling qutrit-like systems, generalizing Schrödinger dynamics, and bridging classical and quantum oscillatory regimes.Keywords Extended complex numbers; Aktas numbers; phase weave; multicarrier oscillations; carrier decomposition; generalized trigonometric functions; higher roots of i; roots-of-unity projectors; delayed symmetry; layered wavefunctions.
BORA AKTAŞ (2025) studied this question.