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Where is the error in this argument

  1. Feb 16, 2013 #1
    It is possible to do this and it is correct:

    [tex]
    \log \left[\sqrt{i}\right] = \log\left\{\exp\left[\frac{i}{2}\left(\frac{\pi}{2}+2\pi n\right)\right]\right\} = \frac{i}{2}\left(\frac{\pi}{2} + 2\pi n\right) = i\left(\frac{\pi}{4} + \pi n\right)
    [/tex]

    But:

    [tex]
    \log \left[i^2 \right] = \log\left\{\exp\left[2i \left(\frac{\pi}{2}+2\pi n\right)\right]\right\} = 2i \left(\frac{\pi}{2} + 2\pi n\right) = i\left(\pi + 4\pi n\right)
    [/tex]

    yet

    ## \log \left[i^2 \right] = \log \left[-1 \right] = i\left(\pi + 2\pi n\right) \ for \ k \in \mathbb{Z}## which is the correct argument.
     
  2. jcsd
  3. Feb 16, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    I'm not sure what your argument really is. Sure (sqrt(i))^4=(i)^2=(-1). (sqrt(-i))^4 is also (-1). So?
     
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