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Values of complex numbers

  1. Jun 17, 2015 #1

    I'm facing a problem finding the values of complex numbers, I'll put two examples then I'll explain the issue.

    ex1: [tex] (-e)^{iπ} [/tex] , my answer is [tex] (-e)^{π^2±2mπ^2} [/tex] The book answer is [tex] (-e)^{π^2} [/tex]

    ex2: [tex] e^{2 arctanh(i)} [/tex] , my answer is [tex] e^{[iπ/2±mπ/2]} = ie^{±mπ/2} [/tex] The book answer is [tex] i [/tex]

    just to mention that the book answer are exactly like wolfram alpha's answers, the problem is that the answers were set as m=0 while they didn't do the same thing for other problems, When can I set m=0 and when I cannot do that?
  2. jcsd
  3. Jun 17, 2015 #2


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    2017 Award

    Staff: Mentor

    Keep the m if you need some logarithm or inverse trigonometric function somewhere, unless the problem statement specifies the branch you are supposed to use.
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