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Math Help - Show this function obeys the Cauchy Riemann equations

  1. #1
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    May 2009
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    Show this function obeys the Cauchy Riemann equations

    f(z) = sin(2z). I have so far got to:

    f(x + iy) = sin[2(x+iy)
    f(x + iy) = sin(2x) cos(2iy) + cos(2x) sin(2iy).

    I'm stuck on converting this into the form f(x + iy) = u(x,y) + iv(x,y).

    Any help on that step? After that step I should be ok.
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  2. #2
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    I haven't tried to work it all out but I would suggest that you write \sin(x)=\frac{e^{ix}-e^{-ix}}{2i}.
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