Squeeze Theorem/Sequences/Complex Numbers

Theorem
Let $\sequence {a_n}$ be a null sequence in $\R$, that is:
 * $a_n \to 0$ as $n \to \infty$

Let $\sequence {z_n}$ be a sequence in $\C$.

Suppose $\sequence {a_n}$ dominates $\sequence {z_n}$.

That is:
 * $\forall n \in \N: \cmod {z_n} \le a_n$

Then $\sequence {z_n}$ is a null sequence.

Proof
Thus $\sequence {z_n}$ is a null sequence.