find a polynomial function that has these zeros

Question

4 and -3i

Answer 1

The complex conjugate of a complex zero must also be a zero, so you will have 3 zeros:

4

-3i

3i

f(x) = A(x - 4)(x + 3i)(x - 3i) = A(x - 4)(x² + 9),

where A is real and A ≠ 0.