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Complex Analysis

  1. May 16, 2009 #1
    How does one show that z^{1/3} is not unique in the complex plane?

    [ Similarly for z^(1/2) and ln(Z) ]


    Thanks,

    Daniel
     
  2. jcsd
  3. May 16, 2009 #2

    HallsofIvy

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    Write z as [itex]re^{i\theta}[/itex] in "polar form". Then [itex]z^{1/3}= r^{1/3}e^{i\theta/3}[/itex]. Now [itex]e^{i(\theta+ 2\pi)}= e^{i\theta}[/itex] but [itex]e^{i(\theta+ 2\pi)/3}[/itex] is not the same as [itex]e^{i\theta/3}[/itex].
     
  4. May 16, 2009 #3
    Thanks :)
     
  5. May 21, 2009 #4
    Dear Mentors,

    Could anyone include explanations about the Laurent series, & the Residues & Poles ? Everything for an undergraduate course ?

    I didn't find anything about that on the forum. if there's a good one plz tell me.

    Thank You in Advance

    ----------------
    Yours Truly
    BOB Merhebi
    Astrobob Group
    www.astrobob.tk[/URL]
     
    Last edited by a moderator: Apr 24, 2017
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