Power Factor Conjugate & Phasor (lagging & leading)

Complex S = V x I*.

V = A sin( Wt + beta) ; I = B sin(Wt + phi) ; Theta = (Beta - Phi)

S = (A angle_beta) x (B angle_phi*)

Beta > Phi = we will get an positive reactance of j (positive Theta)

Phi > Beta = we will get an negative reactance of j. (negative (Theta)

Looking at the power phasor diagram, S = P + jQ. j is always positive and its the first quadrant.

I'm confused because regardless of the reactance component the power phasor diagram is always in the first quadrant and therefore j is always positive. How do we know if the circuit is inductance or capacitance driven?

In addition, when we take the conjugate when solving for the complex component what happen to the angles of current and voltage that help us before to determine if its leading or lagging (I as the reference to V).

Talking about the Load,

your reference is always the voltage, then you look at the current angle, if it is less than the voltage angle then your load is inductive and we describe the system as lagging. If current angle is bigger than the voltage then your load is capacitive and system is capacitive.

For S= P+jQ , it is not necessarily always on the first quarter, it will be so if you have inductive load. and it will be in the forth quarter if the load is capacitive.