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Complex sine function

{title2=$\sin(z+2\pi)=\sin z$}

The kernel $2\pi i\mathbb Z$ of the <complex exponential function> gives
$$
\sin(z+2\pi)
=\frac{e^{iz}e^{2\pi i}-e^{-iz}e^{-2\pi i}}{2i}
=\sin z.
$$
The same period appears as the translation generated by the <monodromy of the complex inverse sine>.

Periodicity of the complex sine

Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 4 / 7A / c / Solution

Periodicity of the complex sine ( $sin (z + 2 π) = sin z$ )

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Periodicity of the complex sine (sin(z+2π)=sinz)

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Periodicity of the complex sine ( $sin (z + 2 π) = sin z$ )

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