  We show that almost all sectors of the disc $\{z \in \mathbb{C}: |z|^2\leq
X\}$ of area $(\log X)^{15.1}$ contain products of exactly two Gaussian primes,
and that almost all sectors of area $(\log X)^{1 + \varepsilon}$ contain
products of exactly three Gaussian primes. The argument is based on mean value
theorems, large value estimates and pointwise bounds for Hecke character sums.
