Equation of Hyperbola in Complex Plane/Examples
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Examples of Equation of Hyperbola in Complex Plane
Example: Foci at $3$ and $-3$, Transverse Axis $4$
The hyperbola in the complex plane whose transverse axis is of length $4$ and whose foci are at the points corresponding to $-3$ and $3$ is given by the equation:
- $\cmod {z + 3} - \cmod {z - 3} = 4$
Hyperbola Defined by $\map \Im {z^2} = 4$
The equation:
- $\map \Im {z^2} = 4$
describes a hyperbola embedded in the complex plane.
Hyperbola Defined by $\map \Re {z^2} > 1$
The inequality:
- $\map \Re {z^2} > 1$
describes the area shaded yellow defined by the following hyperbola: