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any nifty trick to computing curl in phaser domain?

Mathematics
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I will write out my problem
Given an Electric Field {4 cos(6*10^8 t- 2z), 3 sin(6*10^8-2z)} Find associated Magnetic Field
using the formula \[H=\frac{1}{j \omega \epsilon} \nabla x E\]

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Other answers:

so we find phaser \[<4 e^{-2zj},-j3e^{-2zj}>\]
of course we are only taking the real component
so we have to find the curl of that
x component \[\partial /\partial y()- \partial/\partial z(y component)\]

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