Based on the asymptotic homogenization method, the local problems related to two-phase periodic fibrous dielectric composites with isotropic and complex constituents are solved. A hexagonal periodicity distribution of the fibers is considered. Explicit formulas for the real and imaginary parts of the effective dielectric properties are derived. Such formulas can be computed for any desired precision related to a truncation order of an infinite system of algebraic linear equations. Two simple analytical expressions are specified for the first two truncation orders. Comparisons with results via other approachess how a good concordance. Hexagonal periodic lattices of acoustic scatterers are useful structures for acoustic applications
