Complex Sequence is Null iff Modulus of Sequence is Null

Theorem
Let $\sequence {z_n}_{n \mathop \in \N}$ be a complex sequence.

Then:


 * $z_n \to 0$




 * $\cmod {z_n} \to 0$

That is:


 * $\sequence {z_n}_{n \mathop \in \N}$ is a null sequence $\sequence {\cmod {z_n} }_{n \mathop \in \N}$ is a null sequence.