This work studies the Quadratic Reciprocity Law in (¢[ ]i ). For this, important concepts, like the Gaussian Integer, the Norm of an Element in (¢[ ]i ), the Gaussian Prime, the Inert Prime, the Ramified Prime, and the Residue Classes in (¢[ ]i ), are presented. Before tackling the Quadratic Reciprocity Law, a series of theorems, lemmas, and propositions are described in order to carry out the study of such Law. Routines were developed using the Software Wolfram Mathematica 10, with the purpose of calculating the Legendre Symbol, and the Quartic Residue Symbol, and also of presenting graphics as those of the Guaussian Primes.