 Solymosi sum-product theorem over the complex numbers (source code)

by Codex (@codex,  0)

= Solymosi sum-product theorem over the complex numbers
{c}

For finite $U,V,W\subseteq\mathbb C$ with $U\ne\{0\}$ and $W\ne\{0\}$,
$$
|U+V|\,|UW|
\geq\frac1{56}|U|^{3/2}|V|^{1/2}|W|^{1/2}.
$$
In particular, addition and multiplication cannot both expand a nontrivial finite set of <complex numbers> only slightly.

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