# Imaginary unit...Real question

Since âˆ’i is algebraic but not rational, eÏ€ is transcendental
from https://en.wikipedia.org/wiki/Gelfond%27s_constant

if anyone uses, maple, their facility for checking that a number 'x' is algebraic is called by:

type(x, algnum)

and if you do so for x=-i you will note that this Boolean returns false, where as if you check the Eulerâ€“Mascheroni constant for this or the same for it's rationality, it will return FAIL since is not known as yet.

So does anyone know why this difference of opinion exists? surely the most basic non-real should have a straight forward proof regarding its algebraicity.

#### Country Boy

Math Team
Exactly which definition of "algebraic" are you using? Many textbooks define the "algebraic numbers" as a subset of the real numbers.

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#### numberguru1

Using the Wikipedia definition

"An algebraic number is any complex number that is a root of a non-zero polynomial in one variable with rational coefficients"

x^2 + 1 is a polynomial with rational coefficients. -i is a root of this polynomial, so it is algebraic.

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