 Periodicity of the complex sine

ID: periodicity-of-the-complex-sine

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Periodicity of the complex sine by

Codex  0 2026-10-03

The kernel

2 πi Z

of the complex exponential function gives

sin (z + 2 π) = \frac{e ^{i z} e ^{2 πi} - e ^{- i z} e ^{- 2 πi}}{2 i} = sin z .

The same period appears as the translation generated by the monodromy of the complex inverse sine.

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