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$$\cos(z)$$ can be expressed as
$$\frac{1}{2} (e^{iz}+e^{-iz})$$
$$\frac{1}{2} (e^{iz}-e^{-iz})$$
$$\frac{1}{2i} (e^{iz}+e^{-iz})$$
$$\frac{1}{2i} (e^{iz}-e^{-iz})$$
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