Determine set of points in the complex plane that satisfies the following equation

Question

Thanks for taking your time.

I've been given the following problem:

Determine and plot set of points in the complex plane that satisfies the following equation

$ |z-2| + |z+2|=5 $

where $ z = x+iy$.

My first approach was to square both sides, but what I ultimately get is the square of a binomial, which when expanded gives me the product of square roots:

$ 2\sqrt{((x+2)^2+y^2)((x-2)^2+y^2)}$

which I don't know what to do with.

Can anyone provide some insight? Tanks!

You should get an equation after your manipulations. Anyway, what does the condition $|z+2|+|z-2|=5$ mean geometrically? — Angina Seng, Oct 21 '19 at 17:57
@LordSharktheUnknown Thanks for your answer. While solving these problems, geometrically I always tend to get a circle. I suspect this might be an elipse but I don't know how to proceed. — l0ner9, Oct 21 '19 at 17:58
@Aqua I'm on it. I can't type faster than I currently am typing. — l0ner9, Oct 21 '19 at 17:59

score 0 · Answer 1 · answered Oct 21 '19 at 17:57

0

Hint:

Do you know what is a geometric meaning of $|z-w|$?
Do you know the definition of particular conic sections?

answered Oct 21 '19 at 17:57

nonuser

90,026

Specifically $|z-w|$? No. As I said, while doing these exercises I usually get equations of circles. I can't
As for the definition, yes I'm aware of it! Thanks for answering.
– l0ner9 Oct 21 '19 at 18:00

Determine set of points in the complex plane that satisfies the following equation

1 Answers1