  We find the exact values of complexity for an infinite series of 3-manifolds.
Namely, by calculating hyperbolic volumes, we show that c(N_n)=2n, where $c$ is
the complexity of a 3-manifold and N_n is the total space of the punctured
torus bundle over S^1 with monodromy 2&1 1&1 ^n$. We also apply a recent result
of Matveev and Pervova to show that c(M_n) \ge 2Cn with C\approx 0.598, where a
compact manifold M_n is the total space of the torus bundle over S^1 with the
same monodromy as N_n, and discuss an approach to the conjecture c(M_n)=2n+5
based on the equality c(N_n)=2n.
