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Hyperbolic Functions cosh(2-3i)

  1. Oct 21, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the real part, the imaginary part, and the absolute value of:

    cosh(2-3i)

    2. Relevant equations



    3. The attempt at a solution

    I know how to write this using exponentials, but when I looked up the answer the book expanded cosh(2-3i) to cosh 2 cos 3 − i sinh 2 sin 3 , how in the world do you get there??

    Thanks for the help
     
  2. jcsd
  3. Oct 21, 2009 #2
    You'll be happy with this answer, I believe.
    If you remember from regular sin and cosine rules, you have the double angle formula:

    sin(a+b) = sina*cosb + sinb*cosa.

    Well, you have equivalent functions for hyperbolic functions:

    sinh(a±b) = sinha*coshb ± sinhb*cosha

    and

    cosh(a±b) = cosha*coshb ± sinha*sinhb

    You are going to use the second one. The ± means that if you use minus in the first ±, you use minus in the second part of the expression as well.
     
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