Combination Theorem for Sequences/Complex

Theorem
Let $\sequence {z_n}$ and $\sequence {w_n}$ be sequences in $\C$.

Let $\sequence {z_n}$ and $\sequence {w_n}$ be convergent to the following limits:


 * $\displaystyle \lim_{n \mathop \to \infty} z_n = c$
 * $\displaystyle \lim_{n \mathop \to \infty} w_n = d$

Let $\lambda, \mu \in \C$.

Then the following results hold: