Monday 26 July 2021

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\[f(x)=a_0+a_1x+\cdots+a_nx^n\]where \(a_0,a_1,\cdots,a_n\) are all integers such that \(f(i+\omega)=0\).
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