Outline: 
What is the Power Factor and Apparent Power? 
Altering the Power Factor of a Load 
Complex Power 
LAGGING Any angle in this quadrant had a net positive reactance and therefore has mostly inductance: Power Factors for loads with impedances in this quadrant are said to be lagging because for these loads the current lags the voltage. So if the pf = ½ lagging, then we know the angle of Z is + 60° 

LEADING Any angle in this quadrant had a net negative reactance and therefore has mostly capacitance: Power Factors for loads with impedances in this quadrant are said to be leading because for these loads the current leads the voltage. So if the pf = ½ leading, then we know the angle of Z is  60° 

If one states that the pf= ½ or pf = 0.30 without stating 'leading' or 'lagging' then there is incomplete information. The power factor must state either leading or lagging. 
Here is a load. Think if this load as a large utility customer, such as Paramount's Great America: If Great America's pf is not close to one, then the utility company has to generate a greater I_{RMS} thus incurring greater transmission line losses. Great America only has to pay for the average power they use, not the losses on the transmission lines. 

Here is the same load with another load in parallel with it: The effective load Z_{T} can now have a power factor equal to one. At the same time no change has been made to the Great America load  no retooling. Thus Great America still pays for same amount of Average Power as before. We will select Z_{1} such that:
