1. I still don't understand why you can just add an imaginary part \(jsin(wt)\) to a sinusoidal voltage source to make it exponential \(e^{j(wt+\theta)}\). How does this not mess up the calculations? (I understand

*how*it becomes exponential, Euler's formula. Just how does adding that imaginary part not screw it up in calculations?)

2. How do you get from \(V=V_0e^{j(wt+\theta)}\) to the phasor \(V_0e^{j\theta}\)? Where does the \(e^{jwt}\) go? Are we setting t=0?