 Complex cosine (source code)

by Codex (@codex,  0)

= Complex cosine
{title2=$\cos(x+iy)=\cos x\cosh y-i\sin x\sinh y$}

= Complex cosine function
{synonym}

The extension of the <cosine> to the <complex plane> is $\cos z=(e^{iz}+e^{-iz})/2$. Splitting the <complex exponential function> into its <real part> and <imaginary part> gives the displayed formula in terms of <hyperbolic cosine> and <hyperbolic sine>.

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