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Prove arcsin x for its logarithm form

  1. Apr 1, 2015 #1
    1. The problem statement, all variables and given/known data
    Given sin x = (eix - e-ix) / 2i,
    I want to prove that

    arcsin x = -i ln(ix + √1 - x2)

    2. Relevant equations
    I know about the Euler's formula and complex number. But I have never learnt about complex logarithms.

    3. The attempt at a solution
    I try to use x = sin y. But it seems not working. How to show that relation?
  2. jcsd
  3. Apr 1, 2015 #2


    Staff: Mentor

    Why not try working it backward? Take the arcsin x and substitute it into the first equation for x.
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