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Identify and sketch the region in the complex plane satisfying

  • #1

Homework Statement



Identify and sketch the region in the complex plane satisfying

[tex]
| \frac{2 z - 1}{z + i} | \geq 1
[/tex]

Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
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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
1
0
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.
 

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