Sequence of Imaginary Reciprocals

Theorem
Consider the subset $S$ of the complex plane defined as:


 * $S := \set {\dfrac i n : n \in \Z_{>0} }$

That is:
 * $S := \set {i, \dfrac i 2, \dfrac i 3, \dfrac i 4, \ldots}$

where $i$ is the imaginary unit.

Then $S$ has the following properties: