  The paper presents a detailed description of the K-theory and K-homology of
C*-algebras generated by q-normal operators including generators and the index
pairing. The C*-algebras generated by q-normal operators can be viewed as a
q-deformation of the quantum complex plane. In this sense, we find deformations
of the classical Bott projections describing complex line bundles over the
2-sphere, but there are also simpler generators for the K_0-groups, for
instance 1-dimensional Powers-Rieffel type projections and elementary
projections belonging to the C*-algebra. The index pairing between these
projections and generators of the even K-homology group is computed, and the
result is used to express the K_0-classes of the quantized line bundles of any
winding number in terms of the other projections.
