# Does this special case of Rayleigh's monotonicity principle hold true for the norms of complex impedances?

Take a dipole made up of a set of nodes (i.e. resistors) $R_1,R_2\ldots,R_n$ that are connected by vertices (i.e. wires) in any given way. Rayleigh's monotonicity law states that the effective resistance of the dipole, $R_\mathrm{eq}$, is an increasing function of each of its variables $R_1,...,R_n$; that is to say that increasing any $R_i$ will amount to an increase in the effective resistance $R_\mathrm{eq}$.

A consequence of this principle is that adding an extra vertex (i.e. a length of wire) within the dipole will always reduce the effective resistance. Indeed, we may consider that the absence of a length of wire is equivalent to the presence of a resistor with infinite resistance. So adding a vertex is equivalent to reducing its resistance from $\infty \ \Omega$ to $0 \ \Omega$. Hence we may apply Rayleigh's monotonicity principle.

I was wondering if this can be generalised to the norms of complex impedances. That is to say, does adding a vertex within the dipole always reduce the norm of the impedance of the dipole?