Proof regarding complex numbers - how to continue?
Solution 1:
Hint
add $$\Longleftrightarrow \dfrac{|z|^2-2\rm{Re}(z\overline{w})+|w|^2}{1-2\rm{Re}(z\overline{w})+|z|^2|w|^2}<1$$ $$\Longleftrightarrow |z|^2-2\rm{Re}(z\overline{w})+|w|^2<1-2\rm{Re}(z\overline{w})+|z|^2|w|^2$$ $$1-|w|^2-|z|^2+|w|^2|z|^2>0$$ $$\Longleftrightarrow (1-|w|^2)(1-|z|^2)> 0$$