Let $\iota$ 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

$$f(x)=a\_0+a\_1x+\dots+a\_nx^n$$

where $a\_0,a\_1,\dots,a\_n$ are all integers such that $f(\iota+\omega)=0$.

My approach was to substitute $(\iota + \omega)$ in place of $x$ and try some expansion but that resulted in nothing.
This question was asked in a 10 marks question of a very popular entrance examination at the 10+2 level.
A rigorous answer is appreciable.
Thank you.