Thread: Sketching regions in the complex plane

Hi all I have the following problem:

Sketch the following region in the complex plane:

|z+1+i| greater than or equal to 1

i worked through the problem and got the solution (x+1)^2 + (y+1)^2 greater than or equal to 1^2

My question is: how is a circle of radius 1 possibly going to be greater than its own radius? if i'm completely wrong, what does the 1^2 represent other than the radius of the circle?

|z+1+i| >= 1

|z-(-1-i)| >= 1

The distance from -1-i is greater than or equal to 1. This is not a circle. It is an entire plane with an open circle removed.

You are close. Your circle is the edge of the solution region. Excepting the switch to cartesian coordinates, your work seems reasonable.

Originally Posted by andrew2322

Hi all I have the following problem:

Sketch the following region in the complex plane:

|z+1+i| greater than or equal to 1

i worked through the problem and got the solution (x+1)^2 + (y+1)^2 greater than or equal to 1^2

My question is: how is a circle of radius 1 possibly going to be greater than its own radius? if i'm completely wrong, what does the 1^2 represent other than the radius of the circle?

The solution is the circle and all points outside the circle as well.