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What is E(t) if the phasor is 1 - j in field E(t) = {Ee^(j omega letter t)}?

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luvgoj | Student, Undergraduate | (Level 2) Honors

Posted May 23, 2013 at 2:48 PM via web

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What is E(t) if the phasor is 1 - j in field E(t) = {Ee^(j omega letter t)}?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted May 23, 2013 at 4:20 PM (Answer #1)

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You need to use Euler's formula for complex exponential functions, such that:

`e^(j*omega*t) = cos(omega*t) + j*sin(omega*t)`

Considering `bar E = Re(bar E) + j*Im(bar E)` yields:

`bar E*e^(j*omega*t) =Re(bar E)*cos(omega*t) -Im(bar E)*sin(omega*t) + j*(Im(bar E)*cos(omega*t) + Re(bar E)*sin(omega*t))`

Hence, evaluating `E(t)` , using Euler's formula for complex exponential functions and the information provided by the problem `E(t) = bar E*e^(j*omega*t)` , yields ` bar E*e^(j*omega*t) =Re(bar E)*cos(omega*t) -Im(bar E)*sin(omega*t) + j*(Im(bar E)*cos(omega*t) + Re(bar E)*sin(omega*t)).`

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