# Definition
We say that $L \in \mathbb{C}$ is the limit of a [[Complex Functions|function]] ($f : D \to \mathbb{C}$), $f$ at $z_{0} \in \mathbb{C}$ if the following holds:

For every $\varepsilon \gt 0$ there exists $\delta \gt 0$ such that, if $\mid z - z_{0} \mid \; < \delta$ then $\mid f(z) - L \mid \; \lt \varepsilon$.
(Then we write $L = \lim_{ z \to z_{0} } f(z)$)

Observe that this uses the absolute value of complex numbers.