From a recent question on putative names for the sum of the real part and the imaginary part of a complex number at SE.DSP (Technical Term for the Sum I + Q), I was wondering whether there are names for the complex quantity $1+i$, which is the smallest of the Gaussian primes. I have checked in my versions of the books:
- André Warusfel : Les Nombres et leurs mystères
- François Le Lionnais : Les Nombres Remarquables
- David Wells: The Penguin Dictionary of Curious and Interesting Numbers
Since it also plays a role in definitions for Gaussian Mersenne numbers ($(1 \pm i)^n-1$ or $-i((1+i)^n-1)$), I hoped it was given a specific name in the literature, and I could not find any so far.