Kanoussis D. Complembers. An Approach of Understanding 2017

Textbook in PDF format

Complex numbers have amazing applications, not only in Mathematics but in many areas of Physics and Engineering as well. In Mathematics complex numbers are used to evaluate certain types of infinite series and real valued improper integrals, while in Physics and Engineering in general, complex numbers help to study the flow of fluids around objects, to analyze Alternating Current Circuits, (a problem of great practical importance), to investigate the propagation of radio waves through various media, etc.
Also several features of complex numbers make them extremely useful in proving various geometrical propositions, in simple and elegant ways. As a striking example, we quote the Cote’s Theorem, (proved in Example 14-8), the proof of which without complex numbers would be extremely difficult if not impossible.
The current text is a complete and self contained presentation of fundamental concepts, definitions, theorems and techniques on complex numbers and has been designed to be an excellent supplementary textbook for all Mathematics, Physics and Engineering students.
The 90 illustrative solved Examples and the 180 characteristic Problems to be solved have been chosen to help students develop a solid theoretical background, broaden their knowledge and sharpen their analytical skills on the subject