Why can't imaginary numbers be irrational?

Hailee Stout

Hailee Stout

Answered question

2022-05-13

Why can't imaginary numbers be irrational?

Answer & Explanation

hi3c4a2nvrgzb

hi3c4a2nvrgzb

Beginner2022-05-14Added 15 answers

If you defined irrational numbers as C Q rather than R Q , then you would be in the uncomfortable position of calling both i + 1 and 2 + π i irrational, even though the first looks almost like a rational, even an integer, whereas the second looks more like what we expect from an irrational.
Instead, it's cleaner to define Gaussian rationals as those complex numbers a + b i where both a and b are rational. So the first example above is a Gaussian rational (in fact a Gaussian integer), whereas the second is not.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?