Gapplet

Given a Gaussian integer a+bi Z[i], we find a maximal ideal containing it. (Here maximal ideals are prime ideals and vice versa.)

It is fact (which we shall not prove) that every ideal of Z[i] is generated by a single element. If you input an integer like 2, it will become clear that it does not generate a maximal ideal in Z[i], although it does generate a maximal ideal in Z.

Input a+bi, e.g., 2+3*I  (the number i is input as I)
find a maximal ideal containing it