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Complex Hyperbolic Property

  1. Feb 16, 2012 #1
    1. The problem statement, all variables and given/known data

    Show: sinh(z + i2(pi)) = sinh(z) using sinh(z) = (ez - e-z)/2

    2. Relevant equations

    3. The attempt at a solution

    So far I have (ex + i(2∏+y) - e-(x+i(2∏+y))/2.

    Need help proceeding from here. My thoughts were to define a z' = x + i(2∏+y) but I don't think that I can then say that it is equal to sinh(z) but rather sinh(z').
  2. jcsd
  3. Feb 16, 2012 #2


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    What is [itex]e^{2 \pi i}[/itex]? Then use the laws of exponents.
    Last edited: Feb 16, 2012
  4. Feb 16, 2012 #3
    Using the trigonometric construction I was able to get to the answer. Thanks a bunch.
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