Complex numbers proofing

LongLifeLearner

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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
1603496312679.png
 
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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??
 
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
 

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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.
 
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
 

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    IMG_0374.JPG
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Good job. It Just finding the right combination or sequence of operations.
 
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