Why is this the case...
Impedance is defined as the ratio of the voltage phasor and a current phasor. For more information on phasors, you can check here.
Basically, a phasor is a complex number, and as such, supports several types of representation, including the rectangular (which is what you expressed) and the polar form or module / angle. If we express the current and voltage as complex numbers, the impedance is a complex number, but you can not say it's a phasor.
Phasors are applied to the analysis of steady state of an electrical circuit. In the case of an inductive circuit, the current is delayed in phase with the voltage, while in a capacitive circuit, the current is advanced in phase with the voltage. How does this relate to the impedance? as the impedance is a complex number, the angle of the same, corresponds to the phase shift between voltage and current.
If this angle is positive, the voltage is ahead of the current, or the current is late with respect to the voltage, so this is an inductive circuit. A similar analysis can be raised to a capacitive circuit.
A positive angle corresponds to a complex number whose real and imaginary parts are positive.
...what do we do when there is both capacitance and inductance present at the load (i.e. RLC network)?
In a circuit containing both capacitive and inductive elements prevails one identity, that is, the circuit will eventually inductive or capacitive, according to the value of the total impedance equivalent.
Is it possible cancel each inductive and capacitive elements? Yes. In this case, it is said that the circuit is in resonance, and from the point of view of the source, is a pure resistive circuit, although containing reactive elements.