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1) Let [itex]x^2-x+1[/itex] be the ideal for [itex]\mathbb{R}[x][/itex] generated by the polynomial [itex]x^2-x+1[/itex]. Show that the quotient ring [itex]\mathbb{R}[x]/(x^2-x+1)[/itex] is isomorphic to the field [itex]\mathbb{C}[/itex] of complex numbers.

2) Show that the polynomial [itex]x^2+x+1[/itex] is irreducible over [itex]\mathbb{Z}_2[/itex].

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# Homework Help: Isomorphic math help

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