If $\large \left|\frac{z_1 + z_2}{z_1 - z_2}\right| = 1$, $z_2 \neq 0$ and $z_1 \neq z_2$. Then what do we know about $\frac{z_1}{z_2}$.

Question

anonymous · Answer

I think we can use Componendo-Dividendo or whatever it's called. 
$$\frac{z_1}{z_2} = \pm 1$$But $z_1 \neq z_2$, so only one case when $z_1 = -z_2$.

anonymous · Answer

Hmm $\Large\frac{z_1}{z_2}$ is purely real.

lgbasallote · Answer

$\large \color{blue}{\mathtt{o}} \color{forestgreen}{\mathsf{h}}$ $\LARGE \color{red}{\mathbb{\LaTeX}} \color{orange}{\mathcal{!}}$

anonymous · Answer

Lol Nice. LGB!

anonymous · Answer

And negative as 1 isn't possible. Only -1.

anonymous · Answer

I think I have it. Thanks! lol

anonymous · Answer

$$\huge \mathsf{\color{goldenrod}{\text{Nice,}}}\quad \mathrm{\color{royalblue}{\LaTeX}}.$$

lgbasallote · Answer

$\huge \color{gold}{\textbf{you're}}$ $\huge  \color{gray}{\mathsf{good}}$