How to calculate phases and power factor of two loads in series
Describe each load as a complex impedance, then simply add them.

The common Ohm's law we usually see is actually a subset of the full law that applies when the impedance is purely resistive.  That simplifies the algebra since there are no complex numbers of phase angles involved.  However, Ohm's law does work with arbitrary impedances in general.

Likewise, two impedances in series present as the sum of the individual impedances.  Parallel impedances work the same as parallel resistances too.

The actual algebraic manipulations to perform computations on arbitrary impedances, as apposed to pure resistances, is significantly more complex, but the higher level equations are the same.