  We propose a possible scheme to interpret the complex expectation values
associated with resonances having the complex eigenenergies. Using the Green's
function for resonances, the expectation value is basically described by the
Breit-Wigner distribution as a function of the real excitation energy. In the
expression of the complex expectation values for resonances, the real part
brings the integral value of the distribution, while the imaginary part
produces the deviation from the Breit-Wigner distribution,which explains a
shift of the peak in the strength from the resonance energy. We apply the
present scheme to the several nuclear resonances of $^{12}$C including the
Hoyle state, and neutron/proton-rich nuclei of $^6$He, $^6$Be, $^8$He, and
$^8$C. In these nuclei, many-body resonances are obtained as the complex-energy
eigenstates under the correct boundary condition using the complex scaling
method, and their nuclear radii are uniquely evaluated. We discuss the peculiar
energy dependence of the strength function of the square radius for the
resonances in these nuclei.
