Answer
$3−4i$
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 polynomial function has a degree of $5$ with real number coefficients.
Therefore, when $3−4i$ is a zero of a polynomial function of degree $5$ with real number coefficients, then $3−4i$ is a zero by the Conjugate Pairs Theorem.
