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Consider distinct points p and q on the unit circle such that the line through p and q is not parallel to the real axis. Let u be the complex number at the intersection of the line through p and q and the real axis:

 


Find a simple expression for  in terms of p and q. Make sure your answer doesn't contain any conjugation!

 Mar 8, 2021
 #1
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u = (p^2 + q^2)/(p + q).

 Mar 10, 2021

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