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I am trying find the simplified expression of this:

∇(E [itex]\cdot[/itex] E)

Where E is the electric field that can written as [itex]E_{0}[/itex](exp(i(kx-ωt))

I know that since the two vectors are the same => E [itex]\cdot[/itex] E = [itex]||E||^{2}[/itex]

Do I take the gradient of the magnitude then? It just doesn't feel right. Or should it be something like 2ik[itex]E_{0}[/itex]^2?

Thank you so much!