  In this paper, a theoretical calculation of thermal di-lepton production rate
(DPR) is reported from a hot and dense, unbounded rotating quark gluon plasma
in the presence of very strong uniform background magnetic field typically
generated at heavy-ion collision experiments. In this extreme magnetic field,
the quarks as well as anti-quarks are approximated to be confined in the lowest
Landau level (LLL). Firstly, I have converted the expression of the quark
propagator in LLL approximation to the momentum space representation. After
that, using the derived quark propagator, the di-lepton production rate is
calculated from the photon polarization tensor (PPT) with the help of the
framework of thermal field theory. The system is first confined in a cylinder
of radius $R_{\perp}$ and then $R_{\perp}$ is taken to be very large in order
to consider the situation of unbounded system. Depending on the charge of
participating quarks, the role of rotation is to alter the chemical potential.
The DPR is suppressed prominently for low invariant mass with respect to the
LLL-approximated non-rotating case that was reported earlier.
