Combination Theorem for Limits of Functions/Complex

Theorem
Let $\C$ denote the complex numbers.

Let $f$ and $g$ be complex functions defined on an open subset $S \subseteq \C$, except possibly at the point $c \in S$.

Let $f$ and $g$ tend to the following limits:


 * $\ds \lim_{z \mathop \to c} \map f z = l$
 * $\ds \lim_{z \mathop \to c} \map g z = m$

Let $\lambda, \mu \in \C$ be arbitrary complex numbers.

Then the following results hold:

Also see

 * Combination Theorem for Continuous Functions