"Imaginary" part of a quaternion With complex numbers, we write $Im(z)$ to denote the imaginary part of a complex number $z$. I was wondering what $Im(q)$, where $q$ is a quaternion, would show: would it be the $i$ part of the quaternion or all of the $i$, $j$, and $k$ parts? And if it shows all three parts, is there a notation for showing each of the individual parts?
In case this is unclear, if $q = 1 + 2i + 3j + 4k$, would $Im(q)$ be $2i + 3j + 4k$ (or possibly the vector $(2, 3, 4)$) or just $2$? And how would you the individual parts $3$ and $4$ separately?

Usually, the imaginary part of $a+bi+cj+dk$ is $bi+cj+dk$. If I want to talk about, say, $c$, then I mention the coefficient of $j$.
