# 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

*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 .

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.

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