Complex Numbers, Exponentials, and Phasors

Summary

Complex number terminology is important in electrical engineering to distinguish a purely imaginary quantity, like the impedance of an ideal inductor, jωL, from the reactance of the inductor ωL. Complex numbers can be plotted in a complex plane where the vertical axis plots the imaginary portion of the complex number, and the horizontal axis plots the real portion of the complex number. Overlaying a unit circle on the complex plane facilitates understanding how complex numbers relate to exponential and trigonometric functions. The conjugate of a complex number is formed by negating the imaginary part. This chapter explores phasors and sinusoidal steady state in electric circuit theory. Phasors are complex numbers that represent a time‐varying sinusoidal signal. They obey Kirchhoff's current law and Kirchhoff's voltage law.