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As far as I know (or I thought I knew), if we have an electric field $$\mathbf{E}=\mathbf{E_0}\cos(\omega t - kx),$$ we can define it as the real part of $$\mathbf{E}=Re(\mathbf{E_0}e^{i(\omega t - ... 1answer 58 views ### Is polarization of a wave just a description of its motion in three dimensions? Since a polarization of the wave is described by complex numbers, we can try to give that mathematical formalism geometrical meaning. With having two different axes, one imaginary and other real, it ... 2answers 1k views ### What does the complex electric field show? We have a complex electric field. Is there any definition for absolute and imaginary part of a complex electric field? What do they stand for? 1answer 213 views ### Are electrodynamics problems in the complex plane relevant to real life? This is a question I asked in Maths SE, and it was suggested I ask it here. This is a direct copy of that question. I have been reading Tristan Needham's excellent Visual Complex Analysis. The end of ... 1answer 59 views ### Phasor representation of voltage in frequency domain In a text on application of electromagnetism in transmission line, there introduces a phasor for the voltage (in frequency domain)$$\tilde{V}(x) = V^+e^{-i\beta x} + V^-e^{i\beta x.} Here $V^+$ ...
Suppose an electric field $E=-\nabla \psi$ where $\psi=-Q\ln r$ where $Q$ is just some constant and I have found its harmonic conjugate to be $-Q\theta+c$ where $c$ is some constant. What does it say ...