Answer
(a) $ -1$
(b) $ i$
(c) $ i$
Work Step by Step
Use the property $i^2=-1$, we have:
(a) $i^{42}=(i^2)^{21}=(-1)^{21}=-1$
(b) $i^{-31}=i(i)^{-32}=i(i^2)^{-16}=i(-1)^{-16}=i$
(c) $\frac{1}{i^{19}}=i^{-19}=i(i)^{-20}=i(i^2)^{-10}=i(-1)^{-10}=i$