Answer
$2-i$ and $-3+i$
Work Step by Step
The Conjugate Pairs Theorem states that when a polynomial has real coefficients, then any complex zeros occur in conjugate pairs. This means that, when $(p +i \ q)$ is a zero of a polynomial function with a real number of the coefficients, then its conjugate $(p –i q)$, is also a zero of the function.
We can notice that the function has a degree of $6$, so it has $6$ complex (including real) zeros. We are given $2$ real zeros and $2$ complex zeros (which are not conjugate pairs). Thus we must have $6-4=2$ zeros remaining. These zeros are: $2-i$ and $-3+i$, the conjugates of $2+i$ and $-3-i$, by the Conjugate Pairs Theorem.
