Identify the simplest polynomial function

Question

Identify the simplest polynomial function having integer coefficients with the given zeros.

4i, 3, −1

Answer 1

The complex conjugate of a complex zero must also be a zero, so you will have 4 zeros:

4i

-4i

3

-1

The polynomial is of degree 4.

f(x) = A(x - 4i)(x + 4i)(x - 3)(x + 1)

where A is a real integer and A ≠ 0.

f(x) = A(x² + 16)(x - 3)(x + 1)

You can expand this to standard form if you wish.