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Homework Help: [Homework Help!] Find the value of z when sec(z) = 3i.

  1. Dec 14, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the value of z when sec(z) = 3i.

    2. Relevant equations

    sec (z) = 1/cos(z)

    3. The attempt at a solution

    I assume that I need to transform into polar coordinates and then use some transformations. I'm really at a loss. If not a solution maybe a few hints to go in the right direction?

    Thanks in advance.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 15, 2009 #2

    HallsofIvy

    User Avatar
    Science Advisor

    Good start. And, since you are working with complex numbers, cos(z)= (eiz+ e-iz)/2. So you have
    [tex]\frac{2}{e^z+ e^{-z}}= i[/itex]
    which can be reduced to
    [itex]e^{iz}+ e^{-iz}= -2i[/itex]
    and that can be converted to a quadratic.

    Don't assume things!

     
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