Definition:Vector Length/Complex Plane

Example of Vector Length

Let $\mathbf v$ be a vector represented in the complex plane $\C$ by the complex number $z = a + b i$.

The length of $\mathbf v$ is defined as:

$\norm {\mathbf v} = \cmod z$

where $\cmod z = \sqrt {a^2 + b^2}$ is the modulus of $z$.