<< Quaternions`;
Exp[Quaternion[1, 0, 0, 0]]

During evaluation of In[81]:= Power::infy: Infinite expression 1/0 encountered. >>

During evaluation of In[81]:= Power::infy: Infinite expression 1/0 encountered. >>

During evaluation of In[81]:= Power::infy: Infinite expression 1/0 encountered. >>

During evaluation of In[81]:= General::stop: Further output of Power::infy will be suppressed during this calculation. >>

During evaluation of In[81]:= $RecursionLimit::reclim: Recursion depth of 1024 exceeded. >>

During evaluation of In[81]:= $RecursionLimit::reclim: Recursion depth of 1024 exceeded. >>

During evaluation of In[81]:= $RecursionLimit::reclim: Recursion depth of 1024 exceeded. >>

During evaluation of In[81]:= General::stop: Further output of $RecursionLimit::reclim will be suppressed during this calculation. >>

During evaluation of In[81]:= $IterationLimit::itlim: Iteration limit of 4096 exceeded. >>

During evaluation of In[81]:= Infinity::indet: Indeterminate expression 0 ComplexInfinity encountered. >>

In[84]:= ScalarQ[x_] = True;
Exp[Quaternion[a, b, c, d]]

Out[85]= Quaternion[E^a Cos[Sqrt[b^2 + c^2 + d^2]], (
 b E^a Sin[Sqrt[b^2 + c^2 + d^2]])/Sqrt[b^2 + c^2 + d^2], (
 c E^a Sin[Sqrt[b^2 + c^2 + d^2]])/Sqrt[b^2 + c^2 + d^2], (
 d E^a Sin[Sqrt[b^2 + c^2 + d^2]])/Sqrt[b^2 + c^2 + d^2]]

Quaternion /:
Sign[a:Quaternion[__?ScalarQ]]:= a / Abs[a]

Quaternion /:
Sign[a:Quaternion[__?ScalarQ]]:= If[Abs[a]==0, 0, a / Abs[a]]

(* fix bug 66775 -- charlesp *)

SignIJK[Quaternion[a_?ScalarQ, b_?ScalarQ, c_?ScalarQ, d_?ScalarQ]] :=
Sign[Quaternion[0, b, c, d]]