VECTOR REPRESENTATION OF IMPEDANCE

Any impedance Z can be represented by a complex number R + jX, where R can be any nonnegative real number and X can be any real number. Such numbers can be plotted as points in the RX half-plane or as vectors with their end points at the origin (0+j0). Such vectors are called impedance vectors.
Imagine how an impedance vector changes as either R or X or both are varied. If X remains constant, an increase in R causes the vector to get longer. If R remains constant and XL gets larger, the vector also grows longer. If R stays the same as X_C gets larger (negatively), the vector grows longer again. Think of point representing R+ jX moving around in the plane, and imagine where the corresponding points on the resistance and reactance axes lie. These points can be found by drawing straight lines from the point R+ jX to the R and X axes so that the lines intersect the axes at right angles. This is shown in Fig. 1 for several different points. Now think of the points for R and X moving toward the right and left or up and down on their axes. Imagine what happens to the point R+ jX and the corresponding vector from 0 + j0 to R+ jX in various scenarios. This is how impedance changes as the resistance and reactance in a circuit are varied.

Fig. 1. The RX impedance half-plane showing some points for specific complex-number impedances.

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