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The complex numbers \(z\) and \(w\) satisfy \(|z| = |w| = 1 \) and \(zw \ne -1\).

 

(a) Prove that \(\overline{z} = \frac{1}{z}\) and \(\overline{w} = \frac{1}{w}\).

 

(b) Prove that \(\frac{z + w}{zw + 1}\) is a real number.

 Mar 23, 2021
 #1
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Hello,

 

If you search this question up on bing, you should find that algebra.com has the answer. I am unfortuanetely not able to get the link for you. Hope this helps!

 

The Math Whiz

 Mar 23, 2021

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