Like the question states, are all quaternions algebraic numbers, i.e. can they be derived from (inverse) exponentiation of rational numbers? This is in my understanding what makes numbers like the imaginary unit algebraic; does this apply to the units j and k as well?
This question may seem extremely simple, but please understand that I don't have a background in formal mathematics and don't even fully understand what quaternions are, I was just wondering about the above and not being able to find the question stated precisely as such.