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A PROBLEM BOOK IN COMPLEX NUMBERS: A collection of 175 fully solved problems
Complex numbers are widely used in Mathematics and its applications in Engineering and in Physics. Electrical engineers use complex numbers to study circuits carrying alternating currents. Mechanical engineers use complex numbers to analyze vibrations and oscillations of mechanical systems. Propagation of electromagnetic waves through various media makes extensive use of complex numbers. In Quantum Mechanics, the fundamental Schrödinger’s equation is a partial differential equation that contains complex numbers.
Furthermore, a thorough knowledge of complex numbers is a prerequisite for the study of complex functions, an important branch of mathematics with many applications both in pure and applied mathematics and in natural sciences.
In my book “Complex Numbers, an approach of understanding” the reader will find a detailed introduction to the complex numbers.
This book contains 175 fully solved problems, on complex numbers and related applications in Geometry and Trigonometry. The first 75 problems, (Basic Level), are rather simple, routine problems, or problems of moderate difficulty, involving ramifications of the basic theory. The rest 100 problems, (Advanced Level), extend the theory, and some of them, require in depth knowledge and considerable ingenuity to be solved.
Complex numbers provide extremely powerful methods and problems very difficult to be solved by traditional methods, become almost “self-evident” when solved using complex numbers. As a characteristic example, Cote’s Theorem, (Advanced Level, Problem 100), is very difficult to be solved by conventional methods, but its proof using complex numbers is almost trivial.
A systematic summary of main theorems and properties of complex numbers is included, at the beginning of the book. Also, since complex numbers and polynomial equations are closely related, we quote some important theorems on polynomials equations and complex numbers.
Furthermore, a thorough knowledge of complex numbers is a prerequisite for the study of complex functions, an important branch of mathematics with many applications both in pure and applied mathematics and in natural sciences.
In my book “Complex Numbers, an approach of understanding” the reader will find a detailed introduction to the complex numbers.
This book contains 175 fully solved problems, on complex numbers and related applications in Geometry and Trigonometry. The first 75 problems, (Basic Level), are rather simple, routine problems, or problems of moderate difficulty, involving ramifications of the basic theory. The rest 100 problems, (Advanced Level), extend the theory, and some of them, require in depth knowledge and considerable ingenuity to be solved.
Complex numbers provide extremely powerful methods and problems very difficult to be solved by traditional methods, become almost “self-evident” when solved using complex numbers. As a characteristic example, Cote’s Theorem, (Advanced Level, Problem 100), is very difficult to be solved by conventional methods, but its proof using complex numbers is almost trivial.
A systematic summary of main theorems and properties of complex numbers is included, at the beginning of the book. Also, since complex numbers and polynomial equations are closely related, we quote some important theorems on polynomials equations and complex numbers.
177 pages, Kindle Edition
Published July 20, 2022
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