  We derive a lower bound for the subword complexity of the base-$b$ expansion
($b\geq 2$) of all real numbers whose irrationality exponent is equal to 2.
This provides a generalization of a theorem due to Ferenczi and Mauduit. As a
consequence, we obtain the first lower bound for the subword complexity of the
number $e$ and of some other transcendental exponential periods.
