  Rotations on the 3-dimensional Euclidean vector-space can be represented by
real quaternions, as was shown by Hamilton. Introducing complex quaternions
allows us to extend the result to elliptic and hyperbolic rotations on the
Minkowski space, that is, to proper Lorentz rotations. Another generalization
deals with complex rotations on the complex-quaternion algebra. Appropriate
quaternionic expressions of differential operators lead to a quaternionic form
of Maxwell equations; the quaternionic expressions of an electromagnetic-field
in two Galilean frames in relative motion are linked by a complex rotation;
some relativistic invariants of electromagnetic waves are deduced, including
their polarization states and their degrees of polarization. Quaternionic forms
of proper Lorentz rotations are applied to polarization optics along with
illustrative examples. Equivalences between relativistic effects and crystal
optics effects are mentioned. A derivation of the triangle inequality on the
Minkowski space is given; the inequality is illustrated by some properties of
partially polarized lightwaves.
