\begin{definition}[Definition:Rational Function/Complex]
Let $P: \C \to \C$ and $Q: \C \to \C$ be polynomial functions on the set of complex numbers.
Let $S$ be the set $\C$ from which all the roots of $Q$ have been removed.
That is:
:$S = \C \setminus \set {z \in \C: \map Q z = 0}$
Then the equation $y = \dfrac {\map P z} {\map Q z}$ defines a function from $S$ to $\C$.
Such a function is a '''rational (algebraic) function'''.
\end{definition}