Comments on: Complex Square Root http://4by12.com/blog/archives/119 by Guy Gur-Ari Sat, 14 Aug 2010 23:42:00 +0000 hourly 1 http://wordpress.org/?v=3.0.1 By: Guy Gur Ari http://4by12.com/blog/archives/119/comment-page-1#comment-6001 Guy Gur Ari Tue, 24 Mar 2009 15:16:51 +0000 http://4by12.com/blog/archives/119#comment-6001 Yes of course. Perhaps the post was not clear. My only point is this: With the reals, the mistake is easy to spot. More importantly, one can work with a definition (sqrt = positive root), using which algebra behaves as you expect. With the complex numbers the mistake is more subtle, and there is no such convenient definition for sqrt. Seemingly innocent manipulations often conceal mistakes, as one must always be careful when crossing the branch cut. Yes of course. Perhaps the post was not clear. My only point is this: With the reals, the mistake is easy to spot. More importantly, one can work with a definition (sqrt = positive root), using which algebra behaves as you expect.

With the complex numbers the mistake is more subtle, and there is no such convenient definition for sqrt. Seemingly innocent manipulations often conceal mistakes, as one must always be careful when crossing the branch cut.

]]> By: jascha http://4by12.com/blog/archives/119/comment-page-1#comment-5999 jascha Tue, 24 Mar 2009 10:24:28 +0000 http://4by12.com/blog/archives/119#comment-5999 uh-oh. I think it might be spreading to the reals! Proof that 1 = -1: sqrt(1) = 1 sqrt(1) = -1 1 = sqrt(1)/sqrt(1) = 1/-1 = -1 uh-oh. I think it might be spreading to the reals! Proof that 1 = -1:

sqrt(1) = 1
sqrt(1) = -1

1 = sqrt(1)/sqrt(1) = 1/-1 = -1

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