Re: Geometric meaning of common solutions of x^2 + y^2 =1 and y=2?

On 31 Mar 2007 13:15:50 -0700, 131208@xxxxxxxxx wrote:

When we find the common solutions of x^2 + y^2 =1 and y=2, we can
easily determine

x = root(3)*i and -root(3)*i , y = 2.

This circle x^2 + y^2 =1 and the line y=2 don't meet each other
geometrically.

Then what's the meaning of the complex solutions of x^2 + y^2 =1 and
y=2 ?

Is there a meaning?????

One obvious answer is that in C^2 (allowing complex coordinates), the
graphs _do_ meet each other, and at exactly 2 points. But the graphs
no longer represent a circle and a line (in the R^2 sense). If we
regard the graphs in C^2 as graphs in R^4, then each graph is a 2D
surface in R^4.

quasi
.

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