May 2011
Intermediate to advanced
852 pages
28h 45m
English
book
Engineering Circuit Analysis: International Student Version, Tenth Edition
by J. David Irwin, R. Mark Nelms
Content preview from Engineering Circuit Analysis: International Student Version, Tenth Edition
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
Start your free trial
Appendix A. 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
Equation 1.
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
The polar form of a complex number A, which is symbolically equivalent to the exponential form, is written as
Equation 2.
and the rectangular representation of a complex number is written as
Equation 3.
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
Equation 4.
Fig. 2 illustrates that this function in rectangular form is a complex number with a unit amplitude.
Figure 1. The exponential form of a complex number.
Figure 2. A graphical interpretation ...