hi everybody i have a question i can't solve $$\left|\frac{Z-W}{1-\overline ZW}\right|=1$$
the question says the above is true ,use it and prove $|Z|=1$ or $|W|=1$
i have tried putting $Z = x +iy$ and $W= a +ib$ and done some math works but it doesnt get to what question wants
thanks alot
$|a+b|^{2}=|a|^{2}+|b|^{2}+2\Re \overset {-} a b$ for any two complex numbers $a$ and $b$. Since $|Z-W|^{2}=|1-\overset {-} Z W|^{2}$ we get $(1-|Z|^{2})(1-|W|^{2})=0$ after some simplifications. Hence $|Z|=1$ or $|W|=1$.