\begin{definition}[Definition:Cauchy Sequence/Complex Numbers]
Let $\sequence {z_n}$ be a sequence in $\C$.
Then $\sequence {z_n}$ is a '''Cauchy sequence''' {{iff}}:
: $\forall \epsilon \in \R_{>0}: \exists N \in \N: \forall m, n \in \N: m, n \ge N: \size {z_n - z_m} < \epsilon$
where $\size {z_n - z_m}$ denotes the complex modulus of $z_n - z_m$.
Considering the complex plane as a metric space, it is clear that this is a special case of the definition for a metric space.
\end{definition}