  Complementarity relations for wave-particle duality are saturated only for
pure, single-quanton, quantum states. For a completely incoherent state, it is
known that wave and particle quantifiers can reach zero, and hence no
information about the wave and particle aspects of the system can be obtained.
This means that the information is being shared with another systems, and
quantum correlations can be seen as responsible for the loss of purity of the
quanton, provided that the quanton is part of a multipartite pure quantum
system. In this paper, by exploring the purity of bi- and tri-partite pure
quantum states, we show that it is possible to obtain complete complementarity
relations. This procedure allows us to create a general framework for obtaining
complete complementarity relations for a subsystem that belongs to an arbitrary
multi-partite quantum system in a pure state. Besides, by some simple examples,
we show that if the predictability measure is changed then the correlation
measure must also be changed in order to obtain complete complementarity
relations for pure cases.
