- #1

MaestroBach

- 49

- 4

- Homework Statement
- Draw the following set in the complex plane: |z - i| + |z + i| = 3

- Relevant Equations
- N/A

I tried saying z = x + iy, then squared both sides so that I would get something that looked like:

|z - i|^2 + |z + i|^2 + |z - i||z + i| = 3, where the first two terms are simple but the third term is what I don't know what to do with. I'm wondering if I'm using the wrong approach.

For that matter, on a simpler part, where I was told to draw |z - 1 + i| = 2, I said z = x + iy and then got |x - 1 + i + iy|^2 = 2^2 (I squared both sides and rewrote z), then said (x-1)^2 + (1 + y)^2 = 4 to get the equation of a circle (which I figured is what I would get from the equation). Did I even do this right?

Appreciate any help, my textbook is trash unfortunately.

|z - i|^2 + |z + i|^2 + |z - i||z + i| = 3, where the first two terms are simple but the third term is what I don't know what to do with. I'm wondering if I'm using the wrong approach.

For that matter, on a simpler part, where I was told to draw |z - 1 + i| = 2, I said z = x + iy and then got |x - 1 + i + iy|^2 = 2^2 (I squared both sides and rewrote z), then said (x-1)^2 + (1 + y)^2 = 4 to get the equation of a circle (which I figured is what I would get from the equation). Did I even do this right?

Appreciate any help, my textbook is trash unfortunately.