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 ...
Get Basic Engineering Circuit Analysis, Tenth Edition now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
