How many elements are in Z[i]/<3+i>. Explain your answer.
Can someone please show me how to find the order of an ideal complex ring?
For this problem, I guess there are 10 elements in the ring.
What you wrote is correct, however, I do not see how it follows from .
Because if you take , for example, then there is non-uniqueness for the division algrorithm.
Notice if then we want . There are choices for but there are only congruence classes.