Gaussian Integers

A Gaussian integer is a complex number whose real and imaginary parts are both ordinary integers, written in the form a plus b times i where a and b are integers and i squared equals negative one. Carl Friedrich Gauss introduced them in his 1832 monograph on biquadratic, or quartic, reciprocity. The Gaussian integers form a unique factorization domain, so every Gaussian integer breaks down into Gaussian primes in essentially one way, and an ordinary positive prime number remains prime among the Gaussian integers exactly when it is congruent to 3 modulo 4, while every prime congruent to 1 modulo 4 factors further into a product of two conjugate Gaussian primes. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/