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Introductory Mathematics for Engineering Applications by Nathan W. Klingbeil, Kuldip S. Rattan

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Complex Numbers in Engineering

CHAPTER 5

5.1 INTRODUCTION

Complex numbers play a significant role in all engineering disciplines, and a good understanding of this topic is necessary. However, it is especially important for the electrical engineer to master this topic. Although imaginary numbers are not commonly used in daily life, in engineering and physics they are in fact used to represent physical quantities such as impedance of RL, RC, or RLC circuit.

Complex numbers are numbers that consist of two parts, one real and one imaginary. An imaginary number is the square root of a negative real number (−1). The square root of a negative real number is said to be imaginary because there is no real number that gives a negative number after it has been squared. The imaginary number is represented by the letter i by mathematicians and by almost all the engineering disciplines except electrical engineering. Electrical engineers use the letter j to represent imaginary number because the letter i is used in electrical engineering to represent current. To remove this confusion, will be represented by the letter j throughout this chapter.

In general, imaginary numbers are used in combination with a real number to form a complex number, a + bj, where a is the real part (real number) ...

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