Gaussian integer
Noun
Meaning
Gaussian integer (plural Gaussian integers)
(algebra) Any complex number of the form a + bi, where a and b are integers.
Examples
All Gaussian integers on such a line are integer multiples of some Gaussian integer h. But then the integer gh ≠ ±1 divides both a and b.) Second, it follows that z and z* likewise share no prime factors in the Gaussian integers.
As a Euclidean domain It is easy to see graphically that every complex number is within units of a Gaussian integer.
As perfect square Gaussian integers If we consider the square of a Gaussian integer we get the following direct interpretation of Euclid's formulae as representing a perfect square Gaussian integers.
For an odd Gaussian prime and a Gaussian integer relatively prime to with define the quadratic character for by: : Let be distinct Gaussian primes where a and c are odd and b and d are even.
If the Gaussian integer is not prime then it is the product of two Gaussian integers p and q with and integers.
Norm of a Gaussian integer The (arithmetic or field) norm of a Gaussian integer is the square of its absolute value (Euclidean norm) as a complex number.