Physical intepretation of the absolute value of impedance
Consider the impedance of a series RLC circuit



Here \$\rm{Re}( Z) = R\$, the resistive part and \$\rm{Im}( Z) = (X_L - X_c)\$, the reactive part.  For a different circuit the real and imaginary may be calculated differently but we can obtain the magnitude of the impedance as follows.

$$|Z| = \sqrt{\rm{Re}( Z)^2 + \rm{Im}( Z)^2}$$. 

Which we get from Pythagoras.  We can get the phase angle \$\phi\$ by noting \$\tan(\phi) = \dfrac{\rm{Im}( Z)}{\rm{Re}( Z)}\$

We need to take note of the polarities, plus or minus, of \$\rm{Re}( Z)\$ and \$\rm{Re}( Z)\$ to ensure we take the correct inverse tangent.