Often a time varying E-field is represented in complex format. I have a simple E-field (uniform in space) given by(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\vec{E}(t)=E_o\cos(\omega t)\cdot\hat{k}[/itex]

or equivalently, the real part of

[itex]\vec{E}(t)=E_o e^{\omega t}\cdot\hat{k}[/itex].

We know the potential is the negative gradient of the E-field.

If we want to calculate the potential of a field represented in the complex notation, do we need first convert to the "real" representation of and then take the gradient?

In other words how do we deal with all the calculations when the field is represented in the complex format.

Thanks

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# Working w/ Complex representation E-field

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