# Edit:

To those voting to close as 'opinion based', the core question (which should satisfy the 'opinion based'-criteria) is this: `Is there any specific reason why an imaginary number can't be classified irrational; additionally, are the properties of traditionally irrational numbers, when on the imaginary-plane, different from those numbers when on the real-plane?`

# Original Post Follows:

I was discussing irrational numbers and mentioned $πi$ when, to my surprise, I was confronted by a colleague who declared that $πi$ was not irrational since irrational numbers have to be *real*. I didn't agree with him, but after some googling, to my surprise he was right.

By current definitions of *irrational*, a number must be real to be irrational. Ironically, *transcendental numbers* are defined as being able to be real or complex.

Online Definitions:

In mathematics, the irrational numbers are all the real numbers which are not rational numbers

In mathematics, a transcendental number is a real or complex number that is not algebraic

Is there any specific reason why an imaginary number can't be irrational (other than the definition of irrational). As far as I know, $πi$ contains all of the properties of an irrational number (other than not being on the *real*-axis).