perplexus.info :: Just Math : Complex Number Puzzle

Complex Number Puzzle (Posted on 2015-11-08)

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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A more confident answer

Comment 2 of 2 |

The last one was incorrect (as was my next attempt: -24/193)

New approach: try to solve for A, B, C.

I assumed A=a(cos(T)+isin(T), B=a(cos(T)-isin(T)), C=c

Long story very short: the solution is -2/9

(I'll fill in the details later.)

Posted by Jer on 2015-11-09 14:11:51

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