  Let $r$ and $s$ be multiplicatively independent positive integers. We
establish that the $r$-ary expansion and the $s$-ary expansion of an irrational
real number, viewed as infinite words on $\{0, 1, \ldots , r-1\}$ and $\{0, 1,
\ldots , s-1\}$, respectively, cannot have simultaneously a low block
complexity. In particular, they cannot be both Sturmian words.
