When we calculated the complex power, we plotted it on a complex plane.

Where we had the real part here and

the imaginary part here and we labeled all the various values.

What we are going to do is take the triangle out of this complex plane and

draw it like this, we see that we have all the same basic measurements.

We have the P, the Q and the absolute value of S corresponding the real power,

reactive power, and the parent power, and the hour angle beta.

All right, our power angle, so,

to remind us of the equation, we use proof finding the, complex power.

I've listed it here and I've put the power triangle, and what we're going

to do is find out how to calculate all these things from the equations.

So here we have the voltage equation and the current equation

with the m cosine of omega T, plus state E and Im cosine of omega T plus theta I.