Equation of Ellipse in Complex Plane/Examples/Foci at -2i, 2i, Major Axis 6

Example of Equation of Ellipse in Complex Plane
The ellipse in the complex plane whose major axis is of length $6$ and whose foci are at the points corresponding to $-2 i$ and $2 i$ is given by the equation:
 * $\cmod {z + 2 i} + \cmod {z - 2 i} = 6$

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


 * Equation of Ellipse in Complex Plane-Examples-Foci at -2i, 2i, Major Axis 6.png

The result follows.