  The symmetry of the pairing state in iron pnictide superconductor
$\mathrm{Ba_{1-x}K_xFe_2As_2}$ is still controversial. At optimal doping ($x
\approx 0.4$), it is very likely $s$-wave, but for $x=1$ there are experimental
and theoretical arguments for both $s$-wave and $d$-wave. Depending on the
choice for $x=1$, intermediate $s+is$ and $s+id$ states have been proposed for
intermediate doping $ 0.4 < x < 1$. In both states, the time reversal symmetry
is broken and a spontaneous magnetization is allowed. In this work we study a
spontaneous magnetization induced by a nonmagnetic defect in the $s+is$ and
$s+id$ states by using a perturbation theory and numerical calculations for the
Ginzburg-Landau free energy functional. We show that the angular dependence of
the magnetization is distinct in these two states due to the difference in
symmetry properties of the order parameters. Our results indicate a possible
way to distinguish between the $s+is$ and $s+id$ pairing symmetries in
multi-band superconductors.
