Complete the sentence below.
If $7+5 i$ is a zero of a polynomial function of degree 5 with real coefficients, then so is
Answer
Final Answer: The conjugate of $7+5i$, which is \(\boxed{7-5i}\), is also a zero of the polynomial function of degree 5 with real coefficients.
Step 1 ：The complex roots of a polynomial with real coefficients always come in conjugate pairs. This is because the coefficients of the polynomial are real numbers, and when you multiply out (a + bi)(a - bi), you get a real number.
Step 2 ：Therefore, if $7+5i$ is a root of the polynomial, then its conjugate, $7-5i$, must also be a root.
Step 3 ：Final Answer: The conjugate of $7+5i$, which is \(\boxed{7-5i}\), is also a zero of the polynomial function of degree 5 with real coefficients.
