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Complex number problem with trig functions

  1. Jan 20, 2015 #1
    1. The problem statement, all variables and given/known data
    Find d^2/dx^2 and both complex number forms for the complex number equation (1+icos(x))/(1-icos(y))

    2. Relevant equations
    1. z=a+bi
    2. re^itheta

    3. The attempt at a solution
    I have multiplied both sides by 1+icosy and gotten as far as (1+icosx+icosy-cosxcosy)/(1+cos^2y) but am going in circles after that. None of the trig identities seem to get me anywhere either.
  2. jcsd
  3. Jan 21, 2015 #2


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    That's an expression, not an equation. There's no equal sign.

    Multiplied both sides of what? Which problem are you trying to solve first?
  4. Jan 21, 2015 #3


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    Is the problem asking you to express the ##\frac {d^2}{dx^2} ## in terms of z and polar representations?
    Are you starting with ##g : \mathbb{R}^2 \to \mathbb{C} : g(x,y) = \frac{ 1 + i cos x }{1-i cos y}=z ##?
    The second derivative should be straightforward.
    If you are simply trying to get into a : z = a+bi : form, your first attempt is sufficient to break the fraction into real (a) and imaginary (b).
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