Using a quantum group version of the Plancherel theorem, we derive
orthogonality relations for matrix coefficients of corepresentations of a
locally compact quantum group. Moreover, we prove that the modular operator and
the modular conjugation that appear in the Tomita-Takesaki theorem can be
expressed in terms of these matrix coefficients. As a consequence, the modular
autmorphism group of a unimodular quantum group can be expressed in terms of
matrix coefficients. As an example, we make this expression precise for the
quantum group analogue of the normaliser of SU(1,1) in SL(2,\mathbb{C}).