Possible lecture error

[Yarnzorrr]

here is a screenshot from one of my lectures talking about how to find active power (P) and reactive power (Q)

He calculates P using 100*10 Cos (30-(-30), which I understand, though the answer he gets is 200W, but whenever I calculate it I get 500 because cos60 = 0.5 and 0.5*1000 is 500.

Just wanting to know what I'm doing wrong.
Thanks.

 

[NascentOxygen]

It does look like it should be 500.

 

[I_am_learning]

Yes, its obviously 500.
Also, VA = Sqrt(Watts^2+Var^2)
1000 ~= sqrt(500^2+866^2)

 

[yungman]

I think it's 500

I use complex number. From the picture of the board:

V=100∠+30 deg = 100(0.866+j0.5)= 86.6+50j
I=10∠-30 deg = 10(0.866-j0.5)= 8.66-j5.

Power =Re[IV]= Re[(86.6+j50)(8.66-j5)]= 749.956-250=500.