Answer
$2-i$ and $-3+i$
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.
$4$ zeros are already given ($2$ real ones, and $2$ complex ones, which are not conjugate pairs), hence there are only $2$ zeros left which are $\overline{2+i}=2-i$ and $-\overline{-3-i}=-3+i$ according to the Conjugate Pairs Theorem.
