  We prove an asymptotically tight lower bound on $|A+\lambda A|$ for $A\subset
\mathbb{C}$ and algebraic integer $\lambda$. The proof combines strong version
of Freiman's theorem, structural theorem on dense subsets of a hypercubic
lattice and a generalisation of the continuous result on tight bound for the
measure of $K+\tau K$ for a compact subset $K\subset \mathbb{R}^d$ of unit
Lebesgue measure and a fixed linear operator $\tau\colon\mathbb{R}^d\to
\mathbb{R}^d$, obtained in our previous work.
