Gaussian numbers: The numbers of the form \(a+bi\) where both \(a\) and \(b\) are integer and \(i^2=-1\) are called Gaussian numbers and are denoted as \(\mathbb{Z}[i]\). Gaussian numbers contain \(0\) and \(1\), can be added, and multiplied, which makes them a ring. Describe all Gaussian numbers which have a multiplicative inverse in \(\mathbb{Z}[i]\), i.e. all those you can divide by.