  We calculate the Plancherel formula for complex semisimple quantum groups,
that is, Drinfeld doubles of $ q $-deformations of compact semisimple Lie
groups. As a consequence we obtain a concrete description of their associated
reduced group $ C^* $-algebras. The main ingredients in our proof are the
Bernstein-Gelfand-Gelfand complex and the Hopf trace formula.
