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Complex Numbers : Argand Diagram

  1. Aug 31, 2007 #1
    On an Argand diagram, sketch the region R where the following inequalities are satisfied:

    l iz + 1 + 3i l less than or equal to 3

    How do you draw this loci?
    Do i manipulate the equation?

    if so i got this :

    l z - ( -3 + i ) l less than or equal to 3i

    But how in the world do you draw this?

    And is :

    ( l iz + 1 + 3i l less than or equal to 3 )= ( l z* + 1 + 3i l less than or equal to 3)

    If so can is it possible to draw the z* loci and relate it to z's loci.

    Any help will be greatly appreciated. Thanks.
     
  2. jcsd
  3. Aug 31, 2007 #2
    z is some complex number of the form x+iy. What is the modulus of l iz + 1 + 3i l? (Hint: Simplify iz + 1 + 3i to the form A+iB and then find the modulus.)
     
  4. Aug 31, 2007 #3
    If i am going to let z = x + yi

    Then i will get the following results :

    l (1-y) + (3 + x)i l Less than or = 3

    if so, do i draw a circle with radius 3, centre ( -1, -3) ?

    So how this feels wrong.
     
  5. Sep 1, 2007 #4

    learningphysics

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    It should be a circle with radius 3, centre (-3,1)... what's the modulus of l (1-y) + (3 + x)i l ?
     
  6. Sep 1, 2007 #5

    learningphysics

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    You should have l z - ( -3 + i ) l less than or equal to 3. so that's just a circle (and everything inside the circle) centered at -3+i.
     
  7. Sep 1, 2007 #6
    k i got it, thanks.
     
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