  We study resonant mode conversion in the PT-symmetric multimode waveguides,
where symmetry breaking manifests itself in sequential destabilization
(appearance of the complex eigenvalues) of the pairs of adjacent guided modes.
We show that the efficient mode conversion is possible even in the presence of
the resonant longitudinal modulation of the complex refractive index. The
distinguishing feature of the resonant mode conversion in the PT-symmetric
structure is a drastic growth of the width of the resonance curve when the
gain/losses coefficient approaches a critical value, at which symmetry breaking
occurs. We found that in the system with broken symmetry the resonant coupling
between exponentially growing mode with stable higher-order one effectively
stabilizes dynamically coupled pair of modes and remarkably diminishes the
average rate of the total power growth.
