Complex voltage across a capacitor

[preet]

Homework Statement

I'm given the power for a capacitor. I know the voltage across the capacitor has a complex component. How do I find the value of the capacitor?

Power (purely reactive) = -50000j VA
Voltage = 200 + 100j V @ 60 Hz

Homework Equations

Power = (V*V) / Z
Impedance of a capacitor = -j / (2*pi*f*C)

The Attempt at a Solution

(200 + 100j)^2 / Z = -50000j
(30000+40000j) / -50000j = Z
-j / (2*pi*f*C) = (0.8 - 0.6j)
-j / (0.8 - 0.6j) = 2*pi*f*C

C -> complex?


I get a complex component in the value of C

 

[fleem]

The voltage and capacitor current are not orthogonal. I think its strange though that the voltage was defined with a non-zero phase... compared to what?? Either that cap has some internal resistance, or there's a mistake in the givens, or you are suppose to assume the stated phase of the applied voltage is a phase from some other unrelated signal (but the cap phase given is NOT relative to that phase!), and therefore normalize the applied voltage to zero phase (which would mean its a bad question, IMO). I wouldn't feel comfortable assuming any of those unless your teacher wants you to notice the cap has internal resistance and has intentionally defined zero-phase as 90 degrees from the current's phase--which is a rather weird thing to do. But then if the teacher specified the cap is "purely reactive" with no real component, yet defined the applied voltage as having a non-zero phase, then its time to ask your teacher what the heck he meant.