\begin{definition}[Definition:Field Norm of Complex Number]
Let $z = a + i b$ be a complex number, where $a, b \in \R$.
Then the '''field norm of $z$''' is written $\map N z$ and is defined as:
:$\map N z := \cmod \alpha^2 = a^2 + b^2$
where $\cmod \alpha$ denotes the complex modulus of $\alpha$.
\end{definition}