Chapter 4 - Polynomial and Rational Functions - 4.6 Complex Zeros; Fundamental Theorem of Algebra - 4.6 Assess Your Understanding - Page 240: 4

$3-4i$

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. Thus, if $3-4i$ is a zero of a polynomial function of degree $5$ with real number coefficients, then $3-4i$ is also a zero.