Combination Theorem for Sequences/Complex/Product Rule

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:


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

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