Definition:Convergent Sequence/Complex Numbers/Definition 1

Definition
Let $\left \langle {z_k} \right \rangle$ be a sequence in $\C$.

$\left \langle {z_k} \right \rangle$ converges to the limit $l$ iff:


 * $\forall \epsilon \in \R_{>0}: \exists N \in \R: n > N \implies \left|{z_n - l}\right| < \epsilon$

where $\left\vert{z}\right\vert$ is the modulus of $z$.