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.