Definition:Field Norm of Complex Number

Definition
Let $z = a + i b$ be a complex number, where $a, b \in \R$.

Then the 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 $\alpha$.

Also defined as
Note that while $\map N z$ is merely one of a number of different norms that can be defined on the complex numbers.

However, this particular instance is usually what is meant when referring to the norm.

Also see

 * Definition:Complex Modulus