Definition:Vector Length/Complex Plane
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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 $z$.