1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Complex Analysis help?

  1. May 8, 2014 #1
    1. The problem statement, all variables and given/known data

    I can't seem to get a few questions involving inverse trigonometric functions and hyperbolic functions. Here is one that I am stuck on:

    Evaluate the following in the form x+iy:

    sinh-1(i/2) = z

    2. Relevant equations

    sinh z = (ez - e-z)/2

    3. The attempt at a solution

    sinh-1(i/2) = z
    sinh (z) = i/2

    This means that i/2 = (ez - e-z)/2

    Let u = ez

    Where do I go from here? I don't know how to deal with the imaginary number.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 8, 2014 #2
    Actually there is a simpler way. Note that ##sinh^{-1}(z)=ln(z+\sqrt{z^2+1})##
     
    Last edited: May 8, 2014
  4. May 8, 2014 #3
    I got the answer. To get the solution, I put all the terms on one side and used the quadratic formula to find the solutions of u. From there, it is easy enough to figure out.

    The final answers are i(Pi/6 +2nPi); i(5Pi/6 +2nPi)
     
  5. May 8, 2014 #4
    Alright glad to hear that you got the answers.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Complex Analysis help?
Loading...