To solve this problem, we use the fact that if a polynomial has rational coefficients, then complex roots appear in conjugate pairs.

Given zeros:

• $-1$
• $5$
• $1$
• $1 - 3i$

Find the additional zeros:

The zero $1 - 3i$ implies that $1 + 3i$ is also a zero because the complex conjugate of $1 - 3i$ must also be a root.

Thus, the additional zero is: $1 + 3i$

Correct Answer:

The correct choice is: $\boxed{1 + 3i}$

Would you like me to go into more details about rational coefficients and conjugate roots?

Related Questions:

1. What happens if a polynomial has only real coefficients?
2. How do you write a polynomial equation given these roots?
3. What is the degree of a polynomial that includes the given roots?
4. How do you find the conjugate of a complex number?
5. What role do imaginary roots play in polynomial factorization?

Tip:

When solving problems with polynomial roots, always check for the complex conjugate property when coefficients are rational.