Equation of Hyperbola in Complex Plane/Examples/Foci at 3, -3, Transverse Axis 4

Example of Equation of Hyperbola in Complex Plane
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:
 * $\cmod {z + 3} - \cmod {z - 3} = 4$

Proof
From Equation of Hyperbola in Complex Plane, the hyperbola whose transverse axis is $d$ and whose foci are at the points corresponding to $\alpha$ and $\beta$ is given by:
 * $\cmod {z - \alpha} - \cmod {z - \beta} = d$


 * [[File:Equation of Hyperbola in Complex Plane-Examples-Foci at -3, 3, Transverse Axis 4.png|400px]]

The result follows.