# Complex number problem with trig functions

1. Jan 20, 2015

### SlushmanIU

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. Jan 21, 2015

### vela

Staff Emeritus
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?

3. Jan 21, 2015

### 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).