I want to write the quaternion $q=2+i+j-5k$ in the form $r+lc$, where $r,~c (\neq 0)$ are real numbers and $l^2=-1$.
We have the following relation $i^2=j^2=k^2=-1$ and $ij=k,\ jk=i,\ ki=j$.
I can't apply these or otherwise.
I think $l$ with $l^2=-1$ is the key point. This is another quaternion unit and we need to construct it.
Any help