Definition:Convergent Sequence/Complex Numbers/Definition 1

Definition
Let $\sequence {z_k}$ be a sequence in $\C$.

$\sequence {z_k}$ converges to the limit $c \in \C$ :


 * $\forall \epsilon \in \R_{>0}: \exists N \in \R: n > N \implies \cmod {z_n - c} < \epsilon$

where $\cmod z$ denotes the modulus of $z$.

Also see

 * Equivalence of Definitions of Convergent Complex Sequence