Reduce to x+iy: Solving for z=cos\theta+isin\theta

[kathrynag]

Homework Statement

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

Homework Equations

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.

 

[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?

 

[kathrynag]

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

 

[gabbagabbahey]

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