- #1

pylauzier

- 20

- 0

## Homework Statement

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

## Homework Equations

|z| = sqrt( x

^{2}+ y

^{2})

## 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}+ y

^{2}= 8

^{2}

I started from there to write my equation for |z+1| + |z-1| = 8 using x's and y's.

(x+1)

^{2}+ y

^{2}+ (x-1)

^{2}+ y

^{2}= 8

^{2}

x

^{2}- 2x + 1 + x

^{2}+2x +1 + 2y

^{2}= 8

^{2}

2x

^{2}+ 2y

^{2}= 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?