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In the question provided, you are given that one of the zeros of the polynomial function \( f(x) \) is \( 4i \), and you are asked to find another zero.

### Key concept:
For polynomial functions with real coefficients, complex roots always occur in conjugate pairs. This means that if \( 4i \) is a zero, its conjugate, \( -4i \), must also be a zero of \( f(x) \).

### Answer:
Another zero of \( f(x) \) is \( -4i \).

Would you like more details on this concept, or do you have any questions? Here are some related questions to explore:

1. What are complex conjugates and why do they occur in pairs for polynomials with real coefficients?
2. How would you find a polynomial if the given zeros include complex numbers like \( 4i \) and \( -4i \)?
3. What is the fundamental theorem of algebra, and how does it relate to the number of zeros a polynomial can have?
4. How do you express a polynomial with complex roots in standard form?
5. Can a polynomial have non-real complex roots if all its coefficients are real?

**Tip**: Always remember that the complex conjugate root theorem applies to polynomials with real coefficients, ensuring symmetry in their complex roots.

Let f(x) be a polynomial function. If one of the zeros of f(x) is 4i, what is another zero of f(x)?

Explore how to find another zero of a polynomial function given one zero as 4i. This solution covers key algebraic concepts including complex conjugates and the fundamental theorem of algebra. Ideal for students in Grades 10-12.

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