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

  1. Sep 12, 2012 #1
    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?
     
  2. jcsd
  3. Sep 12, 2012 #2

    LCKurtz

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    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.
     
  4. Sep 12, 2012 #3
    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.
     
  5. Sep 12, 2012 #4

    LCKurtz

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    So what do you get?
     
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