The book is a completely new and unconventional look at selected problems of classical physics and is intended for people interested in Special Relativity and relativistic electrodynamics. The idea of Special Relativity is based on the invariance of the laws of physics under the transformations belonging to the Lorentz group. These transformations are internal in real space-time. The author found a complex linear transformation that maintains the invariance of the wave equation but requires the complex domain. The results of the research on this transformation are presented in this monograph. For the research, the author constructed a simple mathematical tool equivalent to Geometric Algebra based on the formalism of the well-known matrix calculus. Although the considerations are carried out in full accordance with the postulates of the classical SR, the use of the paravector calculus to describe the basic laws of physics resulted in surprising results. However, this does not mean that these results contradict experiments. The monograph explains how and why complex phenomena are visible to the observer as real. Finally, an outline of the mathematical structure of complex space-time is presented, which is definitely different from Minkowski space.