Cosine function
Function
| definiendum | $\mathrm{\cos}: \mathbb C\to\mathbb C$ |
| definiendum | $\cos(z) := \sum_{k=0}^\infty \frac{(-1)^{k}}{(2k)!}z^{2n} $ |
Discussion
$\theta\in\mathbb R$
| $\cos(\theta) = \frac{1}{2}(\mathrm e^{i\theta}+\mathrm e^{-i\theta}) $ |
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i.e. if $\zeta:=\mathrm e^{i\theta}$, then $\zeta+\overline{\zeta}=2\cos(\theta)$.
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Context
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