Let $i$ be a root of the equation $x^2+1=0$ and let $\omega$ be a root of the equation $x^2+x+1=0$ . Construct a polynomial$$f(x)=a_0+a_{1}x+\cdots +a_n{x}^n$$where $a_0,a_1,\cdots ,a_n$ are all integers such that $f(i+\omega )=0$.