# Homework Help: Identify and sketch the region in the complex plane satisfying

1. Jul 25, 2009

### complexnumber

1. The problem statement, all variables and given/known data

Identify and sketch the region in the complex plane satisfying

$$| \frac{2 z - 1}{z + i} | \geq 1$$

2. Relevant equations

3. The attempt at a solution

2. Jul 25, 2009

### HallsofIvy

Geometrically, |z- a| is the distance from z to a as points in the complex plane so I recommend you try to rewrite the given absolute value in that way. It might help to "rationalize the denominator", multiplying both numerator and denominator by z- i.

3. Feb 26, 2010

### Tzeentch

Let z=x+yi. Now simplify your inequality by: |2z-1| greater than or equal to |z+i|.(multiply out |z+i|). sub z=x+yi into this inequality. You will find that it gives a circle (if not its an ellipse, i may have made a quick error in attempting to answer this). The area outside this graph is your answer.