Show that $|\frac{z-a}{\bar az-zz}|=1$

Asked Oct 14 '17 at 10:20

Active Oct 14 '17 at 10:20

Viewed 1,974 times

Show that $|\frac{z-a}{\bar az-zz}|=1$, if $a$ and $z$ are any complex numbers, where $z$ does not equal $a$ and $|z|=1$

I tried to use the property that $\bar zz = |z|^2=1$ and factorising out a $|z|$ from the denominator but I'm not sure what to do next.

Thanks in advance

asked Oct 14 '17 at 10:20

kjhg

Let $z=i$ and $a=-i$. – Nosrati Oct 14 '17 at 10:26
Does not look very true when $z=\bar a$ ? – Donald Splutterwit Oct 14 '17 at 10:30
$\Big|\dfrac{z-a}{\overline{az}-zz}\Big|=1$ is better! – Nosrati Oct 14 '17 at 10:32
I'm sure this has been asked a few times. – Git Gud Oct 14 '17 at 11:25
Here's a list of similar questions which I'm sure are useful: 1, 2, 3, 4. – Git Gud Oct 14 '17 at 11:37

0 Answers0