Graph inequality in complex plane; negative z value

[merzperson]

Homework Statement

Graph the following inequality in the complex plane: |1 - z| < 1

2. The attempt at a solution

In order to graph the inequality I need to get the left side in the form |z - ...|

|1 - z| < 1

|(-1)z + 1| < 1

|-1(z - 1)| < 1

|-1||z - 1| < 1

(1)|z - 1| < 1

|z - 1| < 1

From here I know how to graph it, but I'm not sure if my procedure is correct. Does this look right?

 

[Dick]

Sure it's correct. |a-b|=|b-a|. The proof is just what you showed. And they are both the distance from a to b.

 

[merzperson]

Thanks, didn't notice that.