  Using an idea of Doug Lind, we give a lower bound for the Perron-Frobenius
degree of a Perron number that is not totally-real. As an application, we prove
that there are cubic Perron numbers whose Perron-Frobenius degrees are
arbitrary large; a result known to Lind, McMullen and Thurston. A similar
result is proved for biPerron numbers.
