Equation of Ellipse in Complex Plane/Examples/Foci at (0, 2), (0, -2), Major Axis 10

Example of Equation of Ellipse in Complex Plane
The ellipse in the complex plane whose major axis is of length $10$ and whose foci are at the points corresponding to $\tuple {0, 2}$ and $\tuple {0, -2}$ is given by the equation:
 * $\cmod {z + 2 i} + \cmod {z - 2 i} = 10$

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:
 * $\cmod {z - \alpha} + \cmod {z - \beta} = d$

The points $\tuple {0, 2}$ and $\tuple {0, -2}$ correspond to the imaginary numbers $2 i$ and $-2 i$ respectively.

The result follows.