**While trying to solve a 3 phase problem. . .**

While trying to solve a 3 phase problem. . .

I realized I could hardly solve a 2 phase problem.

Does everyone agree that a 10 volt source in series with a 1 ohm resistor in series with an opposing 8 volt source gives a current of 2 amps in the resistor?

If so, if the 10 volt source is at an angle of zero degrees and the 8 volt source is at an angle of +90 degrees, does everyone agree that, according to the rules of working with complex numbers, the current through the resistor is now 12.8 amps at an angle of -39.7 degrees?

The trick is that subtracting two vectors A and B, where A is c + jd and B is e + jf, is equal to = (c-e) + j(d-f).

For A, the 10 volt source, c = 10 and d = 0

For B, the 8 volt source, e = 0 and f = 8

The 3 phase problem, still in progress, is more of the same, a lot more.