  Quantum mechanics and classical mechanics are two very different theories,
but the correspondence principle states that quantum particles behave
classically in the limit of high quantum number. In recent years much research
has been done on extending both quantum mechanics and classical mechanics into
the complex domain. This letter shows that these complex extensions continue to
exhibit a correspondence, and that this correspondence becomes more pronounced
in the complex domain. The association between complex quantum mechanics and
complex classical mechanics is subtle and demonstrating this relationship
prequires the use of asymptotics beyond all orders.
