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Absolute value of a complex number

  1. Nov 4, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the real/imaginary parts of sinh(x+yi) and its abs value.


    2. Relevant equations



    3. The attempt at a solution

    I am able to decompose sinh(x+yi) = cosy*sinh(x) + isin(y)cosh(x) - (which is correct according to my book)

    Now finding the absolute value is kind of causing some problems.
    If I'm not mistaken |z| = sqrt(x^2+y^2) = sqrt(z * conj(z) )

    So I'm treating cosy*sinh(x) + isin(y)cosh(x) as a complex number.

    So I multiply ( cosy*sinh(x) + isin(y)cosh(x) ) * ( cosy*sinh(x) - isin(y)cosh(x) ) and I get sqrt( cosy^2*sinhx^2 + siny^2*coshx^2 ) so I would think sqrt( sinhx^2 + coshx^2 ) is the answer. However, it's supposed to be sqrt( sinhx^2 + siny^2)

    Does anyone know what I did wrong?
     
    Last edited: Nov 4, 2007
  2. jcsd
  3. Nov 4, 2007 #2

    Dick

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    Homework Helper

    "sqrt( cosy^2*sinhx^2 + siny^2*coshx^2 )" is right. Your next step isn't. It looks like they express the answer in terms of just sin and sinh. So take the above and replace cos^2(y) by 1-sin^2(y) and cosh^2(x) by 1+sinh^2(x).
     
    Last edited: Nov 4, 2007
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