Prove that if $w,z$ are complex numbers such that $|w|=|z|=1$ and $wz\ne -1$, then $\frac{w+z}{1+wz}$ is a real number.

I tried solving it but I'm stuck. I know that you should multiply by the conjugate of the denominator, but I don't think that simplifies anything? Any help is much appreciated. Thank you so much!

Guest Sep 1, 2020