complex number question

Q) let a,b,c be distinct complex nos. such that |a|=|b|=|c|>0 .
if a+bc , b+ac , c+ab are real numbers then abc = __

Ans.1

a method or a solution would be appreciated.

3 Answers

71
Vivek @ Born this Way ·

* Slight mistake in denominator of Expression (1).

262
Aditya Bhutra ·

nice solution vivek ,

just want to point out that the condition

a+bc = b+ac = c+ab = 0

is not possible since a,b,c are distinct

1
rishabh ·

@vivek you should have directly given this link http://www.artofproblemsolving.com/Forum/viewtopic.php?f=151&t=473251
would have saved you a lot of time.

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