Word Count : 95

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Define a map (\phi:\mathbb{R}[x]\to\mathbb{C}) by (\phi(f(x))=f(i)), where (i^2=-1). For any (f(x),g(x)\in\mathbb{R}[x]), [ \phi(f+g)=(f+g)(i)=f(i)+g(i)=\phi(f)+\phi(g), ] and [ \phi(fg)=(fg)(i)=f(i)g(i)=\phi(f)\phi(g), ] so (\phi) is a ring ________ ____ ___ ___ _________ ________ ___ ______ _____ _____ __________.
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__________ _______ ____ ____ ____ _______ ________ ______ __________ __________.
_______ ___ ___ ___ _______ ______ _________ ______.
_________ _________ _________ _________ ________.
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__________ _____ ______ _________.
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