  We study the effects of the reheating phase on the evolution of complexities
for the primordial curvature perturbation using the squeezed formalism. We
examine the evolution of the out-of-time correlator, the quantum discord, and
circuit complexity, starting from the inflationary epoch to the
radiation-dominated epoch with different reheating scenarios. We find that for
a mode that reenters the horizon after reheating, the effect of a finite
reheating epoch on the characteristic \textit{freeze-in} amplitude of these
primordial complexities can only be distinguished up to three different classes
depending on whether the equation of state parameter: $(i)$ $w_\mathrm{re}=1/3$
$(ii)$ $w_\mathrm{re}<1/3$, or, (iii) $w_\mathrm{re}>1/3$. For reheating with
different EOS within these classes, the final amplitude will be the same --
hence, the detailed signature of reheating with a class on the complexity
measures will be lost. Taking the central value of the scalar spectral index
($n_s=0.9649$) from Planck and the equation of state during reheating
$w_\mathrm{re}=0.25$ as benchmark values, we found that the behavior of the
complexities for all modes smaller than $1.27\times10^{16}\mathrm{Mpc^{-1}}$
can be classified as above. However, for the small-scale modes reentering the
horizon during reheating, the signature of EOS on the evolution of these two
complexities will be embedded in each of the cases separately.
