What is an example of algebraically closed field? What about a counter-example
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What is an example of algebraically closed field? What about a counter-example

[From: ] [author: ] [Date: 11-05-09] [Hit: ]
because x^2 + 1 has no zeros in R (since the zeros are -i and i).http://en.wikipedia.I hope this helps!......
Just trying to get a grasp of what it means. Thanks!

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An algebraically closed field K is a field where any polynomial f(x) in K[x] has a zero in K.

For example, C is algebraically closed by the Fundamental Theorem of Algebra.

On the other hand, R is not algebraically closed, because x^2 + 1 has no zeros in R (since the zeros are -i and i).

Link:
http://en.wikipedia.org/wiki/Algebraical…

I hope this helps!
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