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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 aconsequence, we obtain the first lower bound for the subword complexity of thenumber $e$ and of some other transcendental exponential periods.

On the expansion of some exponential periods in an integer base