Question

If the imaginary unit `i` rational or irrational ?

Answer 1

The set of rational numbers is a subset of the real numbers

`QQ subset RR`

The set of rational numbers are those that are real but not rational

`P = RR-QQ`, (or `P = RR // QQ`)
`P subset RR`

And the real numbers are a subset of the complex number:

`RR subset CC`

And so `i=sqrt(-1) in CC cancel(in) RR => i cancel(in) P`

And so `i` is neither rational nor irrational, as these are reserved for real numbers only.

`i` is complex!