Find the electric field $E(t) = Re \{ Ae^{j\omega t} \}$ in time domain, where A is specified by the following phasors a) $j\hat{x} + (1 - j)\hat{y}$; b) $1 - j$; c) $e^{j\pi/4} - 1$.
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The electric field E(t) can be written as E(t) = Re{Aejωt} = Re{rAej(ωt+θA)}. Using Euler's formula, we can rewrite this as E(t) = Re{rA(cos(ωt+θA) + jsin(ωt+θA))}. Expanding this expression, we get E(t) = rAcos(ωt+θA) + j(rAsin(ωt+θA)). So, the electric field Show more…
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