  Let $G$ be a connected complex simple Lie group, and let
$\widehat{G}^{\mathrm{d}}$ be the set of all equivalence classes of irreducible
unitary representations with non-vanishing Dirac cohomology. We show that
$\widehat{G}^{\mathrm{d}}$ consists of two parts: finitely many scattered
representations, and finitely many strings of representations. Moreover, the
strings of $\widehat{G}^{\mathrm{d}}$ come from $\widehat{L}^{\mathrm{d}}$ via
cohomological induction and they are all in the good range. Here $L$ runs over
the Levi factors of proper $\theta$-stable parabolic subgroups of $G$. It
follows that figuring out $\widehat{G}^{\mathrm{d}}$ requires a finite
calculation in total. As an application, we report a complete description of
$\widehat{F}_4^{\mathrm{d}}$.
