  A complex unit gain graph is a simple graph in which each orientation of an
edge is given a complex number with modulus 1 and its inverse is assigned to
the opposite orientation of the edge. In this article, first we establish
bounds for the eigenvalues of the complex unit gain graphs. Then we study some
of the properties of the adjacency matrix of complex unit gain graph in
connection with the characteristic and the permanental polynomials. Then we
establish spectral properties of the adjacency matrices of complex unit gain
graphs. In particular, using Perron-Frobenius theory, we establish a
characterization for bipartite graphs in terms of the set of eigenvalues of
gain graph and the set of eigenvalues of the underlying graph. Also, we derive
an equivalent condition on the gain so that the eigenvalues of the gain graph
and the eigenvalues of the underlying graph are the same.
