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Determining graphical set of solutions for complex numbers

  1. Jan 4, 2017 #1
    1. The problem statement, all variables and given/known data
    So we have been doing complex numbers for about 2 weeks and there is this one equation I just can't solve.
    It's about showing the set of solutions in graphical form (on "coordinate" system with the imaginary and the real axis). So here is the equation:

    2. Relevant equations
    |(z+i)/z| < 1

    3. The attempt at a solution
    Well, I just don't know how to solve this "thing":biggrin:
    The only thing we did was to picture some other solutions...

    I hope you can help me with this little problem!
    Thx
     
  2. jcsd
  3. Jan 4, 2017 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Write it as ##|z+i| < |z|##.

    What are the graphical/geometric interpretations of the quantities ##|z+i|## and ##|z|##?
     
  4. Jan 4, 2017 #3

    jedishrfu

    Staff: Mentor

    Checkout Geogebra, its an educational software tool for students and it may be able to help you learn more about complex numbers.

    https://www.geogebra.org/
     
  5. Jan 4, 2017 #4
    yeah I know geogebra and I use it quite often, but I haven't been able to figure out how I can view complex numbers...
     
  6. Jan 4, 2017 #5
    Ok that made things a little clearer...but i still can't figure out how |z+i| could look....
     
  7. Jan 4, 2017 #6

    Mark44

    Staff: Mentor

    |z + i| is the same as |z - (-i)|; i.e. the distance between a complex number z and the imaginary number -i. |z| represents the distance from the same z to the origin.
    Edit: Fixed typo pointed out by SammyS.
     
    Last edited: Jan 5, 2017
  8. Jan 5, 2017 #7
    Ok thx guys I managed to solve it!
     
  9. Jan 5, 2017 #8

    Mark44

    Staff: Mentor

    Thanks, SammyS. -i was what I meant. It's fixed in my earlier post now.
     
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