Phasors: Complex Vectors

by tomizzo
Tags: complex, phasors, vectors
 P: 86 I've recently began a course on electromagnetism and have started dealing with complex vectors. I have a couple questions to ask: Regarding the general concept of complex vectors, I am curious what these actually represent. Refer to attached equation. Am I correct to believe that this equation represents a wave as a function of time traveling through 3D space? And even though there are 3 different sinusoidal functions, they represent a single propagating signal? Now moving onto the mathematics, I have a question regarding an example problem. Refer the second equation attached. This equation is a phasor representation of a wave in 2D space. I am having trouble translating this phasor representation into the time domain. I understand how the x component translates into cos(wt) but I am having trouble in understanding how the y component translates. Specifically, I don't understand why it is negative... Attached Thumbnails
 Engineering Sci Advisor HW Helper Thanks P: 7,293 ##A(t)## is the real part of ##(\hat x + j\hat y)e^{j\omega t}##. ##e^{j\omega t} = \cos \omega t + j \sin \omega t##. And ##j^2 = -1##.
P: 86
 Quote by AlephZero ##A(t)## is the real part of ##(\hat x + j\hat y)e^{j\omega t}##. ##e^{j\omega t} = \cos \omega t + j \sin \omega t##. And ##j^2 = -1##.
Ahh, thank you AlephZero. I apparently at times forget about the common frequency within the two components.

Regarding my first question, any insight on that?

Engineering