I am stuck on the following.

Let R={(a+b(-163)^1/2)/2 : a,b are integers and a-b is even}. We know that R is a PID.

Let z=(a+b(-163)^1/2)/2 then show that the cardinality of R/(z) is

(a^2+b^2(163))/4

this is just the magnitude of z squared but I am not sure how to arrive at the conclusion. Any help would be appreciated.

Susan