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Locus

The set of all points satisfying a stated geometric condition.

A locus (plural loci) is the set of every point satisfying some stated condition, usually an equation or inequality in z. Naming a shape as a locus is a shift in viewpoint: instead of drawing a curve and asking what equation it satisfies, you start from the equation and ask what curve or region it traces out.

Examples

  • The locus of points with |z-1|=|z+1| is the imaginary axis.

  • The locus \operatorname{Re}(z^2)=1 traces out a hyperbola in the complex plane.

See also

Half-plane Region
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