Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Whats a way to determine the range of this complex function?

  1. Sep 12, 2012 #1

    jdinatale

    User Avatar

    Describe the range of [itex]p(z) = -2z^3[/itex] for [itex]z[/itex] in the quarter disk [itex]|z| < 1, 0 <[/itex]Arg[itex]z < \frac{\pi}{2}[/itex].

    The answer is the circular sector [itex]|w| < -2[/itex], [itex]-\pi <[/itex]Arg[itex]w < \frac{\pi}{2}[/itex]

    What's a good way of seeing why this is true?
     
    jdinatale, Sep 12, 2012
  2. jcsd
    Phys.org - latest science and technology news stories on Phys.org
  3. Sep 12, 2012 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You certainly aren't going to get ##|w|<-2## and that argument range isn't correct either. Write ##z = re^{i\theta}## and work with that.
     
    LCKurtz, Sep 12, 2012
  4. Sep 12, 2012 #3

    jdinatale

    User Avatar

    I totally agree with you. The answer in the back of the book (which is what I posted in the OP) seems to be incorrect. That's part of the reason why I was confused.
     
    jdinatale, Sep 12, 2012
  5. Sep 12, 2012 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    So what do you get?
     
    LCKurtz, Sep 12, 2012
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook