Find a degree 3 polynomial with real coefficients having zeros 3 and 3i and a lead coefficient of 1. Write in expanded form.

Answer 1

The complex conjugate of any complex zero must also be a zero, so the 3 zeros are

3

3i

-3i

With a leading coefficient of 1, the polynomial is

f(x) = 1(x - 3)(x - 3i)(x + 3i) = (x - 3)(x² + 9)

You expand it further from here if you wish.