Let , where a and b are integers. Define the norm of α, denoted by Ν (α), as N (α)= a2 + 5...

Let , where a and b are integers. Define the norm of α, denoted by Ν (α), as N (α)= a2 + 5b2.

Show that if  and , where a, b, c, and d are integers, then Ν (αβ) = Ν(α)Ν(β).