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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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re: Playing around on the complex plane. | Comment 5 of 6 |
(In reply to Playing around on the complex plane. by Jer)

Jer:  


That is a very cool result, but I assume that it applies only if b and d is non-zero.  The first solution that you found, (2 + 0i, 2 + 0i), has a product that is distance 3 from 1 + 0i.

Steve

  Posted by Steve Herman on 2012-08-30 17:22:13
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