Complex admittances in parallel

When you see resistors, coils, and capacitors in parallel, you should envision the GB (conductance-susceptance) plane.
Each component, whether it is a resistor, an inductor, or a capacitor, has an admittance that can be represented as a vector in the GB plane. The vectors for pure conductances are constant, even as the frequency changes. But the vectors for the coils and capacitors vary with frequency, in a manner similar to the way they vary in the RX plane.

Pure susceptances

Pure inductive susceptances (B_L) and capacitive susceptances (B_C) add together when coils and capacitors are in parallel. Thus, B = B_L + B_C. Remember that BL is negative and B_C is positive, just the opposite from reactances.
In the GB plane, the jBL and jBC vectors add, but because these vectors point in exactly opposite directions—inductive susceptance down and capacitive susceptance up—the sum, jB, will also inevitably point straight down or up (Fig. 1).

Fig. 1: Pure capacitance and pure inductance are represented by susceptance vectors that point straight up and down.