Imaginary curve

In algebraic geometry an imaginary curve is an algebraic curve which does not contain any real points.

For example, the set of pairs of complex numbers $(x,y)$ satisfying the equation $x^2+y^2=-1$ forms an imaginary circle, containing points such as $(i,0)$ and $(\frac{5i}{3},\frac{4}{3})$ but not containing any points both of whose coordinates are real.

单词	Imaginary curve
释义	Imaginary curve 英语百科 Imaginary curve In algebraic geometry an imaginary curve is an algebraic curve which does not contain any real points. For example, the set of pairs of complex numbers $(x,y)$ satisfying the equation $x^2+y^2=-1$ forms an imaginary circle, containing points such as $(i,0)$ and $(\frac{5i}{3},\frac{4}{3})$ but not containing any points both of whose coordinates are real.
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