Category:Complex Sequence is Null iff Modulus of Sequence is Null

This category contains pages concerning Complex Sequence is Null iff Modulus of Sequence is Null:

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

Then:

$z_n \to 0$

if and only if:

$\cmod {z_n} \to 0$

That is:

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