  In this paper, we use a Tsallis holographic dark energy model in two forms,
interacting and non-interacting cases, to acquire some parameters as the
equation of state for the energy density of the Tsallis model in the FRW
universe concerning the complex form of quintessence model. We will study the
cosmology of complex quintessence by revamping the potential and investigating
the scalar field dynamics. Then we analyze ($\omega-\omega'$) and stability in
two cases, i.e., non-interacting and interacting. We will explore whether these
cases describe a real universe by calculating fractional energy density
$\Omega_{D}$ and concerning two parts of the quintessence field effect (
complex and real part ) by considering the real part of this field to be a
slow-roll field. We know that the part in which the fractional energy density
($\Omega_{D} > 1$) does not describe a real universe. Also, we specified an
interacting coupling parameter $b^{2}$ that depends on the constant parameter
of the Tsallis holographic model ($\delta$) with respect to fractional energy
density ($0.73$). Unlike independence between the fractional energy density and
interacting coupling in the real quintessence model, we determine a
relationship among these parameters in this theory. Finally, by plotting some
figures, we specify the features of ($\omega-\omega'$) and ($\nu_{s}^{2}$) in
two cases and compare the result with each other.
