Complex Analysis

  • Thread starter DanielO_o
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  • #1
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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
 

Answers and Replies

  • #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
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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]
 
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