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

1 Answer | Add Yours

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

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)).`

Sources:

We’ve answered 318,935 questions. We can answer yours, too.

Ask a question