# Chapter 5 - Section 5.6 - Complex Numbers; Quadratic Equations in the Complex Number System - 5.6 Assess Your Understanding: 44

The function has three zeros. Since $-i$ and $3+i$ are complex zeros, then their conjugates $-i$ and $3-i$ must also be zeros of the function.

#### Work Step by Step

RECALL: The Conjugate Pairs Theorem states that if $a+bi$ is a zero of a polynomial function with real coefficients, then $a-bi$ is also a zero of the function. The given statement is false since having $i$ and $3+i$ as zeros of a polynomial function with real coefficients means that $-i$ and $3-i$ are also zeros of the function. However, since the polynomial function's degree is three, it only has three zeros.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.