Basic Engineering Circuit Analysis, Tenth Edition

COMPLEX NUMBERS

Complex numbers are typically represented in three forms: exponential, polar, or rectangular. In the exponential form a complex number A is written as

The real quantity z is known as the amplitude or magnitude, the real quantity θ is called the angle as shown in Fig. 1, and j is the imaginary operator which is the angle between the real axis and A, may be expressed in either radians or degrees.

The polar form of a complex number A, which is symbolically equivalent to the exponential form, is written as

and the rectangular representation of a complex number is written as

where x is the real part of A and y is the imaginary part of A.

The connection between the various representations of A can be seen via Euler’s identity, which is

Fig. 2 illustrates that this function in rectangular form is a complex number with a unit amplitude.

Figure 1The exponential form of a complex ...