= Solution
The <photon number> probabilities of a <coherent state> form a <Poisson distribution> with mean $\mu=|\alpha|^2$. Alternatively normal ordering gives $\langle\hat n(\hat n-1)\rangle=\langle\hat a^{\dagger2}\hat a^2\rangle=|\alpha|^4$. Thus
$$
\boxed{\langle\hat n\rangle=|\alpha|^2,\qquad
\langle\hat n^2\rangle=|\alpha|^4+|\alpha|^2,\qquad
\Delta n=|\alpha|,\qquad
\frac{\Delta n}{\langle\hat n\rangle}=\frac1{|\alpha|}.}
$$
The last ratio is defined only for nonzero $\alpha$. At large $|\alpha|$ the absolute fluctuation grows but its size relative to the mean becomes negligible. This is the deterministic intensity limit within <quantum optics>; it does not assert the disappearance of vacuum-scale quadrature noise.
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