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 $5$, so it has $5$ complex (including real) zeros. Since, $4$ zeros are already given, then we have $1$ zero remaining. This zero is: $-i$, the conjugate of $i$, by the Conjugate Pairs Theorem.