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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.