Identify and Sketch the set of points satisfying...?

M

Mike K

New member
|z-1| + |z+1| <= 2.

A substitution of z= x + iy doesn't seem to help me here (I am probably doing something wrong...) can someone help?
I can probably sketch it, I just need help understanding why it's [-1,1]. Logically it makes sense but I want to show more work.
 
|z-1| + |z+1| <= 2

In an equation involving absolute value when you see |x| realize that it can be replaced by x or -x.

So one or more of the following may be true:

(z-1) + (z+1) <= 2 OR -(z-1) + (z+1) <= 2 OR (z-1) - (z+1) <= 2 OR -(z-1) - (z+1) <= 2

Solve all four and you have the complete solutions for z.
 
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