Gaussian integers

Gaussian integers are complex numbers where both the real and imaginary parts are whole numbers, like a + bi, with a and b as integers. Think of them as points on a grid that extend into the complex plane, similar to Cartesian coordinates but confined to integer positions. They form a special number system used in advanced mathematics, especially in number theory, because they help study solutions to equations and properties related to prime numbers in this extended number setting. Essentially, Gaussian integers combine familiar whole numbers with complex numbers in a neat, structured way.