I've been working on a mathematical problem for a few days now. I'm not sure where my math is falling apart. I have an impedance connected in series with a source. In phasor notation, the impedance is 1.2649 at 71.565 degrees. In rectangular, this impedance is .4 + j1.2 . The power factor for this circuit is 0.32 lagging. I would like to make the circuit have a power factor of .98 leading, while retaining the original resistance (.4). One solution is to place a component in parallel that provides reactive compensation. I have attempted the solution in two ways. One is to convert the impedance into admittance, since parallel admittances add together (making the math simpler). The other way is to work through the math of two parallel impedances. When I try the problem via admittance values, I get a final answer that is a capacitor. This makes sense, as any additional real resistance will change the real power dissipation of the total circuit (my goal here is to make sure real power dissipation stays the same, even with power factor correction). When I try the problem via impedance values, my parallel component does not solve to the inverse value of the parallel admittance component I found in my first solution. In fact, when I calculate what the total impedance should be (load in parallel with component), my answer does not equal the inverse of the admittance. The total admittance I get from my first solution is .25 + j0.0508. The total impedance I get from my second solution is .4 - j0.0812. These two values are not inverse of each other. Why is that?