1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Elementary algebra of complex variables problem

  1. Aug 28, 2012 #1
    I'm having difficulty deducing that Re z = 0.

    w00r3b.jpg
     
  2. jcsd
  3. Aug 28, 2012 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Try multiplying the top and bottom by (1-w*).
     
  4. Aug 28, 2012 #3
    Thank you, that seems to work. Can you confirm that this is correct?

    http://i45.tinypic.com/2wc2xl4.png
     
    Last edited by a moderator: Aug 28, 2012
  5. Aug 28, 2012 #4

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You made a minor error in calculating the denominator when you canceled the ones.
     
  6. Aug 28, 2012 #5
    Sorry for butting in, but although I can see where jdinatale went wrong in his last post, I still can't see how Re(z) can be proved to be zero.

    Of course it's correct, but I can't quite see it.
     
  7. Aug 29, 2012 #6

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    The calculation shows z is pure imaginary and that's still true after you make the correction. Doesn't that show Re(z)=0?
     
  8. Aug 29, 2012 #7
    How does it?

    Sorry, I'm probably being very thick here and will live to regret it.

    How does

    [tex]z = (1 + \omega) / (1 - \omega)[/tex]
    where [itex]\omega = e^{ik\pi/50}[/itex]

    imply that [itex]z[/itex] is purely imaginary?

    Like I say, I know it's correct to say so, but I'm lost on how to prove it - even after trying using the conjugate method as offered above.

    It'll probably be a face-palm moment when I find out...
     
  9. Aug 29, 2012 #8

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Look at what happens when jdinatale multiplies by (1+w*). The results has w-w* (which is pure imaginary) in the numerator and w+w* (which is pure real) in the denominator. What kind of a number is imaginary/real?
     
  10. Aug 29, 2012 #9
    Ha-ha! I was right!!!

    A complete face-palm...

    Thanks for that. I blame my incompetence on my getting on a bit. :redface:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Elementary algebra of complex variables problem
Loading...