  We show an analogue of a theorem of An, Ghosh, Guan, and Ly on weighted badly
approximable vectors for totally imaginary number fields. We show that for
$G=\mathrm{SL}_2(\mathbb{C})\times\dots\times\mathrm{SL}_2(\mathbb{C})$ and
$\Gamma<G$ a lattice subgroup, the points of $G/\Gamma$ with bounded orbits
under a one-parameter Ad-semisimple subgroup of $G$ form a
hyperplane-absolute-winning set. As an application, we also provide a
generalization of a result of Esdahl-Schou and Kristensen about the set of
badly approximable complex numbers.
