Complex number problem with trig functions

[SlushmanIU]

Homework Statement

Find d^2/dx^2 and both complex number forms for the complex number equation (1+icos(x))/(1-icos(y))[/B]

Homework Equations

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

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.

 

[vela]

Homework Statement

[/b]
Find d^2/dx^2 and both complex number forms for the complex number equation (1+icos(x))/(1-icos(y))

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

Homework Equations

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

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.

Multiplied both sides of what? Which problem are you trying to solve first?

 

[RUber]

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).