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Math Help - log(z+3i)

  1. #1
    Newbie
    Joined
    Feb 2010
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    7

    log(z+3i)

    hey guys... this is a two part question

    1. where is the log not analytic

    ok so i know its where the Re is less than or equal to 0
    and where the Im =0

    so i preety much just write log(x+iy+3i)
    and equate.. how ever its asking for the log... not the Log

    so how do i do that



    and lastly how woud i take the log(z+3i)

    do i write it as log(re^i@ +3i)

    and do ln(r) +.....??

    thanks for all the help
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  2. #2
    MHF Contributor

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    If z= re^{i\theta}, then log(z)= log(r)+ i\theta. Now think about the fact that adding any multiple of 2\pi does not change z but gives different values for log(z).
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  3. #3
    Newbie
    Joined
    Feb 2010
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    right but theres a brannch line
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