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Complex Number Puzzle (Posted on 2015-11-08) Difficulty: 3 of 5
Each of A, B and C is a complex number such that:

A+B+C = 2, and:
A2 + B2 + C2 = 3, and:
A*B*C = 4

Evaluate:
(A*B + C - 1)-1 + (B*C + A - 1)-1 + (C*A + B - 1)-1

See The Solution Submitted by K Sengupta    
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Some Thoughts Maybe I got it (possible spoiler) | Comment 1 of 2
The given info can be used to get other equations such as
AB+AC+BC=1/2
AB^2+BA^2+AC^2+CA^2+CB^2+BC^2=2
etc

If you get a common denominator for the expression to be evaluated and expand like crazy you get a big algebra mess, but all of the pieces can be rearranged and refactored and end up as
(8+1/2)/(-(40+3/4)) = -34/123

Which is the solution assuming I made no errors. 

  Posted by Jer on 2015-11-08 11:26:25
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