A 4 dimensional extension of [[Complex Numbers]]. #### Identities $\huge a+bi+cj+dk$ $\huge\begin{align} i^2=j^2&=k^2=-1 \\ \end{align}$ $\huge \begin{array} iij =k & jk = i & ki=j \\ ji=-k & kj=-i & ik = -j \end{array}$ $\huge ijk = -1 $