Suppose that a polynomial function of degree 4 with rational coefficients has $-3+5 i, 5-\sqrt{2}$ as zeros. Find the other zeros.

Step 1 ：Suppose that a polynomial function of degree 4 with rational coefficients has \(-3+5 i, 5-\sqrt{2}\) as zeros.

Step 2 ：The polynomial function of degree 4 with rational coefficients means that if it has irrational or complex roots, they must come in conjugate pairs. This is due to the fact that when you multiply out \((x - (a + bi))(x - (a - bi))\), the result is a polynomial with rational coefficients.

Step 3 ：Therefore, if the polynomial has a root of \(-3+5 i\), it must also have a root of \(-3-5 i\). Similarly, if it has a root of \(5-\sqrt{2}\), it must also have a root of \(5+\sqrt{2}\).

Step 4 ：Final Answer: The other zeros are \(\boxed{-3-5 i, 5+\sqrt{2}}\)