Complex Numbers in Electronics
Complex numbers extend the real numbers by adding an additional term called imaginary. This two-dimensionality makes it possible to simplify the understanding and calculations of many mathematical and physical questions.
This article explains the basic fundamentals of complex numbers and their main applications for the particular case of electronics [1][2] and communications [3][4]. The table of contents is as follows:
This section lays the foundation for a correct understanding of the relevance of complex numbers in electronics [1][2] and communications [3][4]. After a concise explanation of the most generic theory, Euler’s Formula and its relation to the basic trigonometric functions, sine and cosine, are introduced. With this knowledge, the possible representations of a complex number are revealed, whose choice is key to solve more easily the mathematical calculations needed in each application.
A complex number is obtained by adding two elements: a real term and an imaginary term. As its name suggests, the real part consists of a real number. On the other hand, the imaginary part is obtained by multiplying a real number by the imaginary operator j. For example, a and b being two real numbers, the next number, c, is complex:
