We have investigated properties of the positional numeration system with . We proved that every Gaussian integer has a unique -NAF representation in this system, which is always optimal and an average digit of such a representation has only a probability to be non-zero. We have also calculated the maximum number of optimal representations a Gaussian integer can have if its -NAF representation has exactly non-zero digits, as well as which exact Gaussian integers achieve this maximum. The result is similar to that in [num-binary-signed-reprs], except with a different recurrent sequence, given by
with the maximum number of optimal representations for a given being .