Logarithm in Complex Numbers

Abstract

In the present manuscript a first approach to the study of logarithm of complex numbers is discussed. In order to do so, we start with the fact that the logarithm function is the inverse of e^z, in complex numbers. It is noted that this last function is not “one to one” and therefore a specific branch is required to have a function that has an inverse. The function Arg is defined in the complex numbers known as the function that relates a complex number with a number in [0,2?) that corresponds to the angle that forms the segment that goes from the origin to the complex number with the positive axis x, in the positive sense, counter-clockwise