  Here is a Python code that performs a 1D inversion of Magnetic Susceptibility from Frequency-Domain Electromagnetic (FDEM) data, assuming a fixed electrical conductivity, using the provided APIs:
```python
import numpy as np
from SimPEG import Mesh, Maps, SolverLU, SolverPardiso
from SimPEG.EM import FDEM
from SimPEG.EM.FDEM import Survey, Problem
from SimPEG.EM.FDEM.Utils import plot_data_misfits

# Set up the mesh
cs = 10.0
npad = 10
hx = [(cs, npad, -1.3), (cs, 100), (cs, npad, 1.3)]
hy = [(cs, npad, -1.3), (cs, 100), (cs, npad, 1.3)]
mesh = Mesh.CylMesh(hx, hy, '00D')

# Define geologic parameters and electrical conductivity
k0 = 1e-2
mu_r = 1e-2

# Set up the relative magnetic permeability
mu_0 = 4e-7 * np.pi

# Define mappings and set up the FDEM problem and survey
survey_type = 'dipole-dipole'
frequencies = np.logspace(1, 4, 100)
src_locations = np.array([[0.0, 0.0, 0.0], [0.0, 0.0, 100.0]])
receiver_locations = np.array([[0.0, 0.0, 0.0], [0.0, 0.0, 100.0]])
survey = Survey.from_locations(survey_type, src_locations, receiver_locations, frequencies)
problem = Problem.from_survey(survey, mesh, {'k0': k0, 'mu_r': mu_r, 'mu_0': mu_0})

# Set up the inversion
inversion = ComplicatedInversion(problem, {'k0': k0, 'mu_r': mu_r, 'mu_0': mu_0})

# Set up the solver
solver = SolverPardiso if PardisoSolver else SolverLU

# Run the inversion
inversion.run(solver=solver)

# Plot the conductivity model, the permeability model, and the data misfits
if plot_data_misfits:
    plot_data_misfits(inversion.model, survey, problem, mesh)
```
Note that this code assumes that the `PardisoSolver` module is available, and it will fall back to the `SolverLU` module if `PardisoSolver` is not available. You can modify the code to use a different solver by changing the `solver` argument in the `inversion.run()` method.