$-i$, $3+2i,$ and $-2-i$
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 $6$, hence it has $6$ complex (including real) zeros. $3$ zeros are already given, hence there are only $3$ zeros left which are $-i$, $3+2i$ and $-2-i$ (the conjugates of $i$, $3-2i$, and $-2+i$, respectively) $according to the Conjugate Pairs Theorem.