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Foundations of Electromagnetic Compatibility with Practical Applications by Bogdan Adamczyk

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6Complex Numbers and Phasors

6.1 Definitions and Forms

A complex number z is a number that can be expressed as

where x and y are real numbers and

(6.2)images

x is called a real part of z, and we write x = Re(z).

y is called an imaginary part of z, and we write y = Im(z).

j is called an imaginary unit, sometimes expressed as images.

As we will soon see, there are several equivalent representations of complex numbers. The representation in Eq. (6.1) is called the rectangular form.

When dealing with complex numbers, it is often expedient to represent them graphically. We can easily do that in a complex plane using a Cartesian coordinate system, where the x axis is the real axis and the y axis is the imaginary axis, as shown in Figure 6.1.

image

Figure 6.1 Complex plane.

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