  We prove results on complex interpolation of vector-valued Sobolev spaces
over the half-line with Dirichlet boundary condition. Motivated by applications
in evolution equations, the results are presented for Banach space-valued
Sobolev spaces with a power weight. The proof is based on recent results on
pointwise multipliers in Bessel potential spaces, for which we present a new
and simpler proof as well. We apply the results to characterize the fractional
domain spaces of the first derivative operator on the half line.
