Define $\displaystyle N:Z[w] \rightarrow Z by N(a+bw) = a^2 - ab + b^2 $ with $\displaystyle w = \frac {-1}{2} + \frac {3^{1/2}}{2}i $.

Show that N is multiplicative.

I'm a bit rusty on this, showing it is multiplicative means closure, associative, inverse, identity, right? Or N(ab) = N(a)N(b)?