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Why is the complex projective planes the most natural place to look to consider solutions of polynomial equation?

Why is the complex plane $\mathbb{C}$ adequate for polynomial equations of one variable? Is this because the Riemann sphere is topologically similar to $\mathbb{C}$?

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    Why have you asked several questions, and not accepted answers to any of them? If you don't like the answers, why do you keep asking questions? If you don't know about accepting answers, why haven't you read the faq?2011-11-05
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    Oh, I didn't know about that. I have accepted the previous good answers now. :)2011-11-05

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