Electronic – Need device with poor power factor

Now, part (b) and (c) seem easy enough to answer given enough information but I cannot figure out whether I'm understanding (a) right.

The question reads to me as if part(a) applies before the correction so....

Try looking up power factor phasor diagrams: -

You have an apparent power (volt*amps or VA) of 150 and, you have an angle of 24 degrees. Just apply pythagoras to calculate real (active) power. As bonus you can even calculate reactive power.

I would say that the most general formula is:

$$P=Re\{\underline{S}\}=Re\{\underline{V}·\underline{I}^{\star}\}=S\cos{\theta}$$

where I'm using underline to identify phasors.

S is the module of \$\underline{S}\$ and it is always positive (it is simply the voltage amplitude times the current amplitude).

\$\theta\$ is the angle between voltage and current. If this angle is bigger than 90º it means that the load is in reality providing active power to the source and not the other way around.

Therefore P can be positive or negative.