- Thread starter
- #1

#### sweatingbear

##### Member

- May 3, 2013

- 91

Here's a fun problem proof I came across. Show that

\(\displaystyle \left| \frac { z- w }{1 - \overline{z}w} \right| < 1\)

given \(\displaystyle |z|<1\), \(\displaystyle |w|<1\). I attempted writing z and w in rectangular coordinates (a+bi) but to no avail. Any suggestions, forum?

\(\displaystyle \left| \frac { z- w }{1 - \overline{z}w} \right| < 1\)

given \(\displaystyle |z|<1\), \(\displaystyle |w|<1\). I attempted writing z and w in rectangular coordinates (a+bi) but to no avail. Any suggestions, forum?

Last edited by a moderator: