1. ## Sketching complex sets

I'm trying to sketch the following complex set:

|z-1|+|z-1|=2

I have tried replacing z=x+yi, but I'm getting nowhere with that approach.

I'm finding it difficult to visualise as I'm not sure what the solution looks like.

Thanks!

Tony

2. Originally Posted by Tony2710
I'm trying to sketch the following complex set:
|z-1|+|z-1|=2
Are you sure about that problem?
You have typed the same expression twice.

3. Sorry, the problem is:

|z-1|+|z+1|=2

4. An ellipse is a set of points such that the sum of the distances from two fixed points is constant.
That is the situation here. The two fixed points are 1 & -1.