If the imaginary unit $i$ rational or irrational ?

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Answer 1 · 2017-02-19T02:56:24

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!

If the imaginary unit ii rational or irrational ?