In a circuit with a voltage source in series with a capacitor, inductor, and resistor, will the complex power of the capacitor and inductor be in phase?
No they won't. If you just consider the simpler circuit of a source with a parallel capacitor and parallel inductor i.e. no series resistor, the current flow in the capacitor is exactly 180 degrees opposite to the current flow in the inductor.
Adding the resistor makes things a little less than 180 degrees and, if the resistor totally dominated that limb impedance wise then the best you would see is a 90 degree difference between capacitor current and "the other current".
For my definition of complex power I've used this wiki article.