Equation of Hyperbola in Complex Plane/Examples

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: