  The generator coordinate method of a microscopic cluster model is developed
to treat the resonance and scattering of nuclear clusters with complex scaling.
We consistently derive the formulation of the complex scaling for the
microscopic cluster model, in which only the relative motions between clusters
are transformed in the generator coordinate wave function. We also reveal the
applicability of this method to the cluster wave function. Furthermore, we
demonstrate this framework in the 2$\alpha$ system of $^8$Be and obtain the
solutions of resonance and non-resonant continuum states. Using these
solutions, we calculate the level density, which brings the phase shifts of the
cluster-cluster scattering. This work becomes the foundation in the description
of the multi-cluster scattering states of nuclei in a microscopic framework
with complex scaling.
