## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$-i$ and $-2i$
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 degree of $5$, so it has $5$ complex (including real) zeros. Since, $3$ zeros are already given, then we have $2$ zeros remaining. These are: $-i$ and $-2i$, the conjugates of $i$ and $2i$, by the Conjugate Pairs Theorem.