Geometric position of a complex set. I'm quite struggling with this question and help would be appreciated.

Define the geometric position of a complex set:

$|z-4i| +|z+4i|=10$
Translate to geometry: the sum of the distances from $z$ to the two points $4i$ and $-4i$ is $10$. We recognize this an ellipse with foci $\pm 4i$.
put $z=x+iy$

$|x+iy+4i|+|x+iy-4i|=10$

$|x+i(y+4)|+|x+i(y-4)|=10$

you know $|a+ib|=\sqrt{(a^2+b^2)}$

so $\sqrt{(x^2+(y+4)^2)}  +\sqrt{(x^2+(y-4)^2)=10}$
 it is ellipse