How are phasors obtained from real values in AC?

[yosimba2000]

Ok, so I know phasors are based on Euler's Formula: e^j*(X+phi) = cos(X+phi) + jsin(X+phi)

But how do we use real value like V(t) = Acos(V+phi) in Euler's Formula?

V(t) has no imaginary component, so how can we write the phasor of this as A<phi, where phi is the angle between real and imaginary axis?

I guess what I'm really asking is the "derivation" of real values to another representation that uses imaginary numbers..

 

[tech99]

For a series circuit, you have to use current as the reference in the circuit, and then express the voltage across each component in degrees relative to that. For a parallel circuit the converse. It can be done graphically if preferred, using a phasor diagram, and this is a good way to understand what is going on.