With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

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 ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

No credit card required