Question

Find a polynomial function f in standard form with zeros 3i, -2, 1

Answer 1

The first thing to remember is that when you have a zero of 3i, you will also have a zero of -3i. This is because of the way imaginary solutions are created (taking the square root of a negative number). When you take the sqrt you get TWO answers.
The factors for these zeros are (x - 3i)(x+3i)(x+2)(x-1)
When you multiply the factors, the polynomial will be:
x^4 + x^3 + 7x^2 + 9x - 18