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Complex Conclusion (Posted on 2012-08-29) Difficulty: 3 of 5
Each of a and c is a positive integer and each of b and d is an integer with b ≥ d.

Determine all possible pairs (a + bi, c + di) of complex numbers whose sum equals their product.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts re: Solution | Comment 3 of 6 |
(In reply to Solution by Jer)

Nice work, Jer.  I agree with your answer, but I have two nits to pick:

a) You haven't shown that there are no solutions where exactly one of b and d is 0.  This is easy enough to do.  For instance, if d = 0 and b is non-zero, then c = 1 and a = a +1, so there is no solution.

b) At one point you start out assuming that b and d have the same sign, calculate that bd = -1, and reach a solution that violates your assumption.  Upon getting to bd = -1, you should just conclude that there are no solutions where b and d have the same sign.

  Posted by Steve Herman on 2012-08-29 15:17:23
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