Impedance IS an imaginary number, calculate it out. Its based on the magnetic field of the coil, NOT the resistance of the wire, hence why it is not called impedance, NOT resistance.
Impedance = sqrt(R^2 + (xl-xc)^2) is the equation you use to find total impedance in a circuit using a capacitor, inductor and a resistor. A resistor has a REAL resistance and is not imaginary, a capacitor and inductor has imaginary resistance called impedance. Resistance uses the symbol R impedance uses the symbol Z, there is a reason they uses separate designations.
A cap is not physically connected whatsoever between the two leads. It is two plates separtated by a dialetric. There has to be a connection between the plates for there to be resistance. Sure a peice of wire, the coil in an inductor has resistance to dc current, but not to AC current, with AC current, the opposing magnetic feilds in the wire creates a resistance of its own. A coil has some capacitance, but at low frequencies its very small. Hence Xc=1/2*pi*frequency*farad if you calculate that for say 80Hz, a low frequency, the value of the cap will be high in resistance, at a high frequency say 20kHz the cap will have a low resistance. Two opposing wires separated by a dialetric, which can be air, can be a capacitor including a speaker coil. So if there is so little capacitance in the coil, the sqrt(R^2 + (xl-xc)^2) equation doesn't really make much of a difference, you might as well omitt it, its such a small number in that case.
The equation for impedance in a coil is:
Z=j*(omega)*L
Z=impedance
j=an engineering notation for the square root of -1 (AN IMAGINARY NUMBER), a lower case letter, so it is not mixed up with J or joules.
omega=which is time OR 2*pi*frequency
L=the inductance of a coil
Calculate it out, and YES you need a calculator that can do imaginary numbers, probably a scientific calculator.
I KNOW my electronics.