What is the Finite Field Order of Z[i]/A in Z[i] with A=<1+i>?

[missavvy]

Homework Statement

If A=<1+i> in Z, show that Z/A is a finite field and find its order

Homework Equations

The Attempt at a Solution

Not sure where to start...

Z/A = {m+ni + A, m, n integers} ? is that right?

And I don't know what else to do.

 

[micromass]

Maybe you can use that 2=(1+i)(1-i)...