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Homework Help: Help me solve this equation.

  1. Sep 7, 2010 #1
    1. The problem statement, all variables and given/known data
    Find all the values of Z which satisfy the equation, Z being a complex number in the form x+i*y.


    2. Relevant equations
    Every trig identity out there.


    3. The attempt at a solution
    Here's what I got so far:

    Cosh(z) = i*Cos(3)
    Cosh(x)*Cos(y)+i*(Sinh(x)*Sin(y)) = i*Cos(3)

    Therefore,

    Cosh(x)*Cos(y) = 0
    Sinh(x)*Sin(y) = i*Cos(3)

    y = Pi/2 (since there's no value of x which can give Cosh(x) = 0). y may also be Pi/2 + 2nPi, where n is an integer.

    Therefore,
    Sinh(x) = i*Cos(3)

    But I don't know how to proceed from there.
     
  2. jcsd
  3. Sep 7, 2010 #2
    Use the identity sinh(x) = .5[exp(x)-exp(-x)]. Identities for sinh(x), and cosh(x) can be found on wikipedia.
     
  4. Sep 7, 2010 #3
    I have thought of using that, but I don't know how to get the values for x from there. Would you be so kind to tell me how?
     
  5. Sep 7, 2010 #4
    Sure. After we replace sinh(x) with .5[exp(x)-exp(-x)], lets first multiply both sides of the equation by 2, then by e^x. Set everything equal to zero (isolate all terms on one side) which should yield:
    [tex]e^2^x-something*e^x-1=0[/tex]
    Can you see what to do from here?
     
  6. Sep 7, 2010 #5
    I think I just saw it. I get:

    [tex]e^2^x-e^x*2cos(3)-1 = 0[/tex]

    which stinks of quadratic equation.Things could get messy with that cos(3), though, but I'll take a shot. Thanks a lot, dude!
     
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