I've recently began a course on electromagnetism and have started dealing with complex vectors. I have a couple questions to ask:(adsbygoogle = window.adsbygoogle || []).push({});

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...

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# Phasors: Complex Vectors

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