We have investigated properties of the positional numeration system with β=i1,𝒟={0,±1,±i}. We proved that every Gaussian integer has a unique 3-NAF representation in this system, which is always optimal and an average digit of such a representation has only a 14 probability to be non-zero. We have also calculated the maximum number of optimal representations a Gaussian integer can have if its 3-NAF representation has exactly N 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

r13,r08,r117,rN+3rN+2+2rN+1+2rN,

with the maximum number of optimal representations for a given N being rN3.