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Log of Complex Variable

  1. Jun 16, 2012 #1
    what is log of z=X+JY?

    Thanks
     
  2. jcsd
  3. Jun 16, 2012 #2
    Did you try to find out what it would be??

    Here.
     
  4. Jun 16, 2012 #3

    HallsofIvy

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    We can always write x+ iy in "polar form": [itex]x+ iy= re^{i\theta}[/itex] where [itex]r= \sqrt{x^2+ y^2}[/itex] and [itex]\theta= arctan(y/x)[/itex].

    Then [itex]ln(x+ iy)= ln(re^{i\theta})= ln(r)+ i\theta[/itex]. Of course, because tangent is periodic, with period [itex]\pi[/itex], ln is not a single-valued function:
    [itex]ln(x+ iy)= ln(r)+ i(\theta+ n\pi)[/itex] for n any integer.
     
  5. Jun 16, 2012 #4
    Thanks
     
  6. Jun 16, 2012 #5
    ln(x+iy)=ln(r)+i(θ+2*nπ) for n any integer.
     
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