Maxwell Equations

                                                                         (1)

There are sixteen equations describing 14 field quantities.

To cast these in quaternion form it’s easiest to write the quaternions in vector-scalar format. Write the quaternion
  as

                                                                                                                         (2)

where  q is the three-vector  in ordinary three dimensional space. e_x e_y e_z are Cartesian unit vectors.

Multiplication of two quaternions A and B is

                                                      (3)

Define a quaternion gradient operator:

                                                                                                                           (4)

                                                                    (5)

                                                  (6)

So, in summary, define quaternions M and N and S as:

                                                        (7)

Then the Maxwell equations of (1) are equivalent to the quaternion equations:
                                                                                                                       (8)

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