  In addition to rather complicated general methods it is interesting and
valuable to develop fast efficient methods for calculating generators of power
integral bases in special types of number fields. We consider sextic fields
containing a real cubic and a complex quadratic fields. We develop a very
simple and very efficient method to calculate generators of power integral
bases in this type of fields. Our method can be applied to infinite families of
number fields, as well. We substantially improve the former methods. Our
algorithm is illustrated with detailed examples, involving infinite parametric
families.
