Identify and sketch the region in the complex plane satisfying

[complexnumber]

Homework Statement

Identify and sketch the region in the complex plane satisfying

<br /> | \frac{2 z - 1}{z + i} | \geq 1<br />

Homework Equations

The Attempt at a Solution

 

[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.

 

[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.