Solution
= Solution
The <Solymosi sum-product theorem over the complex numbers> states that if finite $U,V,W\subseteq\mathbb C$ satisfy $U\ne\{0\}$ and $W\ne\{0\}$, then
$$
\boxed{|U+V|\,|UW|
\geq\frac1{56}|U|^{3/2}|V|^{1/2}|W|^{1/2}.}
$$
= Solution
The <Solymosi sum-product theorem over the complex numbers> states that if finite $U,V,W\subseteq\mathbb C$ satisfy $U\ne\{0\}$ and $W\ne\{0\}$, then
$$
\boxed{|U+V|\,|UW|
\geq\frac1{56}|U|^{3/2}|V|^{1/2}|W|^{1/2}.}
$$