Phasor Math and AC Circuits Mathematically, phasors behave a lot like exponential numbers. This is not a coincidence; treated as complex numbers, a phasor like 23 ∠ 40° is really 23 40°i , where i is the imaginary square root of negative one. What you need to know is that when you multiply two phasors, the amplitudes multiply, but the angles add. For instance, (5 ∠ 30°)·(7 ∠-45°) = 35 ∠-15° because 5·7=35, and 30+-45=-15. When you divide phasors, the amplitudes divide, but the angles subtract (top minus bottom). (8 ∠ 50°)/(2 ∠ 60°) = 4 ∠-10° because 8/2=4 and 50-60=-10. Unfortunately, the only time you can directly add or subtract two phasors is if they have the same angle. You can add two reactances like this: -4 90°+-11 90° = -15 90° , but you cannot simply add a resistance such as 3 0° directly to a reactance such as -2 90° . Instead, you must combine them to create an impedance: ! Z
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