  In light of the recent observations of type Ia supernovae suggesting an
accelerating expansion of the Universe, we wish in this paper to point out the
possibility of using a complex scalar field as the quintessence to account for
the acceleration. In particular, we extend the idea of Huterer and Turner in
deriving the reconstruction equations for the complex quintessence, showing the
feasibility of making use of a complex scalar field (instead of a real scalar
field) while maintaining the uniqueness feature of the reconstruction for two
possible situations, respectively. We discuss very briefly how future
observations may help to distinguish the different quintessence scenarios,
including the scenario with a positive cosmological constant.
