What are complementary genes? Does this inheritance pattern obey Mendel's second law?

Complementary genes are the different genes that act together to determine a given phenotypical trait.

For instance, consider a phenotypical trait conditioned by 2 complementary genes whose alleles are respectively X, x, Y and y. performing the hybridization in F2 4 the different phenotypical forms are obtained: X_Y_ (double dominant), X_yy (dominant for the first pair, recessive for the second), xxY_ (recessive for the first pair, dominant for the second) and xxyy (double recessive). This is what happens, for instance, regarding the color of budgerigar feathers, in which the double dominant interaction results in green feathers, the dominant for the first pair, recessive for the second interaction results in yellow feathers, the recessive for the first pair, dominant for the second interaction leads to blue feathers and the double recessive interaction leads to white feathers.

Every complementary gene segregates independently from the others since they are located in different chromosomes. Thus the pattern follows the Mendel's second law (although it does not obey Mendel's first law).