1. The problem statement, all variables and given/known data I'm asked to describe geometrically the set of points in the complex plane describing some equations. I got them all right except this one: |z+1| + |z-1| = 8 2. Relevant equations |z| = sqrt( x2 + y2 ) 3. The attempt at a solution Well, I know that an equation of the |z+1| = 8 type would be a circle centered at (-1,0) with a radius of 8. Such a circle has the following equation: (x+1)2 + y2 = 82 I started from there to write my equation for |z+1| + |z-1| = 8 using x's and y's. (x+1)2 + y2 + (x-1)2 + y2 = 82 x2 - 2x + 1 + x2 +2x +1 + 2y2 = 82 2x2 + 2y2 = 14 I end up with the equation of a circle, but the solution manual says the solution is an ellipse of foci (-1,0), (1,0), semi-major axis = 4. What did I do wrong?