Answer
$\left(x^5-6x^4+13x^3-12x^2+4x\right)+i\left(x^4-6x^3+13x^2-12x+4\right)$
Work Step by Step
Since the polynomial function should have degree $5$ and we are given only $3$ zeros, it means we have zeros of multiplicity greater than $1$.
For example:
$$\begin{align*}
f(x)&=(x-1)^2(x-2)^2(x-(-i)))\\
&=(x^2-2x+1)(x^2-4x+4)(x+i)\\
&=(x^4-6x^3+13x^2-12x+4)(x-i)\\
&=\left(x^5-6x^4+13x^3-12x^2+4x\right)+i\left(x^4-6x^3+13x^2-12x+4\right).\end{align*}$$
