Imaginary Number, Phasor Analysis

[ixtabstudios]

With phasors I thought the current (cos) was rotated 90° and so the cos has the j to show this rotation

[camgere]

@ixtabstudios I agree the current is rotated by 90 degrees from the voltage.

sin(theta) = cos(pi/2 - theta). So I'm not sure about your statement about j. I'd have to see the example worked out in detail. It is really easy to get off by pi/2 or pi, there are lot's of clever identities involved.

Thanks for watching.

[camgere]

You are right.

The cosine term is generally the Real part and the sine term is generally the Imaginary part.

At 1:17 Euler's formula should be

Ae^(j(wt+a)) = A cos(wt+a) + iAsin(wt+a) where w = omega and a = alpha

At 1:47 it should be

Im(Ae^(j(wt+a)) = Asin(wt+a)

Complex numbers often have an interesting visual interpretation. I try to show a bit of that. It's too bad they are often used as tricky test questions.

Good catch.

[Abba2six]

At 1:47, why is the real part a sine function and not a cosine function? Thanks for the explanation btw.