Hi guys, not sure if this is the correct forum for Rings but I'll try it here anyways

I'm working on exam questions and I am very lost. Any help or pointers on the following would be really appreciated as I'm running out of revision time!

Q1

Let R be the subring of C defined by R={a+2bi e Z[i]:a,b e Z}.

Show that the set I={2m+2ni e R: m,n e Z} is an ideal of R.

Show that I is not a principal ideal of R

Q2

Let f(x)=x^3+x+2 e Z_5[x] and let I=<f(x)>. How many distinct cosets of I are there?

In q1 I think you can look at the elements 2 and 2i in I to show that it is not a principal ideal?

Thanks!