On generalized Jørgensen inequality in $\mathrm{SL}(2, \mathbb{C})$

Wang, Jiang and Cao have obtained a generalized version of the Jørgensen inequality in Proc. Indian Acad. Sci. Math. Sci., 123(2):245–251, 2013, for two generator subgroups of $\mathrm{SL}(2, \mathbb{C})$ where one of the generators is loxodromic. We prove that their inequality is strict.