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}=___?