$-i$ and $-2i$
Work Step by Step
The Conjugate Pairs Theorem says that if a polynomial has real coefficients, then any complex zeros occur in conjugate pairs. That is, if $a + bi$ is a zero then so is $a – bi$ and vice-versa. Its degree is $5$, hence it has $5$ complex (including real) zeros. $3$ zeros are already given, hence there are only $2$ zeros left which are $-i$ and $-2i$ (the conjugates of $i$ and $2i$, respectively) according to the Conjugate Pairs Theorem.