find a group isomorphic to ℤ 1. Knowing the below proof, The group of units of ℤ is isomorphic to a familiar group. Which one? 2. We have already shown: "Let R be a ring with unity, and let U denote the set of units in R. Show that U is a group under the multiplication in R." Also, ℤ has been defined as the set of all complex numbers of the form a+bi, where a,b∈ℤ. 3. Does it have something to do do with the homomorphism Norm(a+bi)=a^2+b^2? I don't think so, because Norm is not an isomorphism, right?