>>11818656The complex field is simply the cartesian product of the real field with itself, equipped with specially defined binary operations that make it into a field.
It turns out that the frequency information of signals can be encoded into the complex field from the real field using the laplace transform, this is the main idea behind most complex number usage in EE.
Ill give you a simple example so you can see how exactly using complex numbers help encode frequency and phase info.
Suppose you have a circuit working with ac voltage, as we know, ac voltage can be thought of as a cosine function, that is , now, if you have a ciruit in which each component is working under the same angular frequency, then the only important transformation that occurs to your signal when going thru each component in the circuit is a phase transformation, which equates to either integration or differentiation depending on the direction of the shift, and those 2 operations correspond to either division of multiplication on the complex field, this is very important and it becomes apparent from the following equations:
Hope this helps!
