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An addition to my last post... I had the intention to check a possible source before posting, and forgot... I just checked my library, and if you can find a copy of the book "Five Fingers to Infinity", edited by Frank Swetz, there is an article about the slow acceptance of complex numbers by Phillip Jones, on page 369, and on pg 374 there is an illustration from Wallis 1693 Algebra in Latin that shows Wallis' approach to the complex solutions of a quadratic, which is a very geometric version of the same idea you are speaking of. Sorry I didn't get this in the original... -Pat Ballew, for the T2T service
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