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 $ijk = i^2 = -1$

If you put $\;q=a+bi+cj+dk\;$ , then
$$\begin{align*}qi=ai-b-ck+dj\\
iq=ai-b+ck-dj\end{align*}$$
Well, what do you deduce about the coefficients $\;a,b,c,d\in\Bbb R\;$ above?
