Quaternion identity proof If $q \in \mathbb{H}$ satisfies $qi = iq$, prove that $q \in \mathbb{C}$
This seems kinda of intuitive since quaternions extend the complex numbers. I am thinking that $q=i$ because i know that $ij = k , ji = -k$, which is expand to all combinations of $i,j,k,$ which I think means that I have to use $ijk = i^2 = -1$

Any complex number $q$ satisfies $q i = i q,$ so it is not true that $q=i$ However, just writing $q = a + b i + c j + d k,$ and writing down $q i$ and $i q$ ought to do the trick.
