# Reduce to x+iy

1. Feb 1, 2009

### kathrynag

1. The problem statement, all variables and given/known data

Reduce to x+iy
$$\frac{1+z}{1-z}$$ where z=cos$$\theta$$+isin$$\theta$$.

2. Relevant equations

3. The attempt at a solution
$$\frac{1+z}{1-z}$$
Multiply by conjugate
$$\frac{1+2z+z^{2}}{1-z^{2}}$$
When I plug in the z value nothing seems to cancel out.

2. Feb 1, 2009

### gabbagabbahey

You seem to have multiplied both the numerator and denominator by $(1+z)$....but that isn't really the complex conjugate of $(1-z)$ is it?....Don't you actually want to multiply by $(1-\bar{z})$ instead?

3. Feb 2, 2009

### kathrynag

So i should multiply by 1+(costheta+isintheta)?

4. Feb 2, 2009

### gabbagabbahey

No, $1-z=(1-\cos\theta)-i\sin\theta$, so $\overline{1-z}=$___?