  Disorder in two-band superconductors with repulsive interband interaction
induces a frustrated competition between the phase-locking preferences of the
various potential and kinetic terms. This frustrated interaction can result in
the formation of an $s+is$ superconducting state, that breaks the time-reversal
symmetry. In this paper we study the normal modes and their associated
coherence lengths in such materials. We especially focus on the consequences of
the soft modes stemming from the frustration and time-reversal-symmetry
breakdown. We find that two-bands superconductors with such impurity-induced
frustrated interactions display a rich spectrum of physical properties that are
absent in their clean counterparts. It features a mixing of Leggett's and
Anderson-Higgs modes, and a soft mode with diverging coherence length at the
impurity-induced second order phase transition from $s_{\pm}/s_{++}$ states to
the $s+is$ state. Such a soft mode generically results in long-range attractive
intervortex forces that can trigger the formation of vortex clusters. We find
that, if such clusters are formed, their size and internal flux density have a
characteristic temperature dependence that could be probed in
muon-spin-rotation experiments. We also comment on the appearance of
spontaneous magnetic fields due to spatially varying impurities.
