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Show that arcsin(2) is

  1. May 16, 2013 #1
    Got a maths exam tomorrow been looking through some past papers. Have hit a stumbling block with regard to complex numbers, the problem lies with my algebra.

    1. The problem statement, all variables and given/known data
    Show that [itex]\arcsin(2) = \frac{\pi}{2}-i\ln (2\pm \sqrt3)[/itex]


    2. Relevant equations
    I'm fairly certain the way to solve this is to use
    [tex]\sin(z)=\frac{1}{2i}(e^{iz}- e^{-iz})[/tex]


    3. The attempt at a solution
    Equating sin(z) to 2 I could only rearrange it to

    [tex]4i=e^{iz}-e^{-iz}[/tex]
    I was always pretty awful at algebra and can't see a way to rearrange for z. If anyone could nudge me in the right direction it would be greatly appreciated.
     
  2. jcsd
  3. May 16, 2013 #2
    The problem becomes simpler if you make the substitution [itex]v=e^{iz}[/itex].
     
  4. May 16, 2013 #3

    haruspex

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    When the question says "show that a=b", it gives you the option of working from the other end.
     
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