Complex numbers proofing

[LongLifeLearner]

Hello. I did tried to do an exercise sound as below:
if a, b are any complex numbers, and |z|=1, prove that |((az+b)/(conjugate bz+conjugate a))=1

I do started with the properties of |z|^2=z* conjugate z but i end out no end solution . Pls kindly assist. Tq

 

[pka]

I simply cannot read this question. [A new image has been posted]
Here are some facts: \(\dfrac{1}{z}=\dfrac{\overline{~z~}}{|z|^2}\), \(\left(\overline{~\dfrac{z}{w}~}\right)=\dfrac{\overline{~z~}}{\overline{~w~}}\),
\(~\&~\overline{~z\cdot w~}=\overline{~z~}\cdot\overline{~w~}\)
Can you clarify your post??

 

[LongLifeLearner]

I simply cannot read this question. [A new image has been posted]
Here are some facts: \(\dfrac{1}{z}=\dfrac{\overline{~z~}}{|z|^2}\), \(\left(\overline{~\dfrac{z}{w}~}\right)=\dfrac{\overline{~z~}}{\overline{~w~}}\),
\(~\&~\overline{~z\cdot w~}=\overline{~z~}\cdot\overline{~w~}\)
Can you clarify your post??

Sorry for confusing you. Here i attached with the original question

 

[Dr.Peterson]

Hello. I did tried to do an exercise sound as below:
if a, b are any complex numbers, and |z|=1, prove that |((az+b)/(conjugate bz+conjugate a))=1

I do started with the properties of |z|^2=z* conjugate z but i end out no end solution . Pls kindly assist. Tq
View attachment 22550

You made at least one mistake in your work, when you dropped the bar over the b in the second factor in the denominator, under a longer bar.

I'm not sure whether your approach will lead to a proof or not. And it's very hard to discuss your work when you seem to have made several different starts, with no explanation.

 

[LongLifeLearner]

_Hello

You made at least one mistake in your work, when you dropped the bar over the b in the second factor in the denominator, under a longer bar.

I'm not sure whether your approach will lead to a proof or not. And it's very hard to discuss your work when you seem to have made several different starts, with no explanation.

Thank you for the mistake found. I get it as per attached

 

[pka]

Good job. It Just finding the right combination or sequence of operations.

 

[LongLifeLearner]

Good job. It Just finding the right combination or sequence of operations.

Thanks. Found it very interesting.