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let A and B be two complex number such that A/B+B/A =1 prove that the origin and the two points represented by A and B form vertices of an equilateral triangle

let A and B be two complex number such that  A/B+B/A =1 prove that the origin and the two points represented by A and  B form vertices of an equilateral triangle

Grade:12

1 Answers

mycroft holmes
272 Points
10 years ago


The triangle with origin, A and B as vertices will have side lengths |A|, |B| and |A-B|.

 

We will prove that |A| = |B| = |A-B|.

 

 

Similarly 

 

From the above two relations we immediately obtain that 

 

Hence, 

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