It is true that sqrt(1) = 1 if you are using the principle square root function, but you only specify that later, not in the "proof". I was merely trying to point out that you were wrong when you said that for a=a to imply that sqrt(a)=sqrt(a) we need to take the principle square root. There are two possible roots, one where we do have that sqrt(x^y) = x^(y/2)(ie. sqrt(i^4) = i^2)and one where sqrt(1) = 1.
I am not trying to say that you were wrong, obviously the problem is with the sqrt step. It's just that the way you put it seemed misleading, at least to me. What I was trying to say is that it is not necessary to assume that sqrt is the principle square root function. I probably should have written something like "There is actually nothing wrong with taking the general square root of a complex number".
There is actually nothing wrong with taking the square root of a complex number. The problem is that the sqrt(x) can be x or -x. After taking sqrt(i^4) = sqrt(1), you get +/- i^2 = +/- 1.
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It is true that sqrt(1) = 1 if you are using the principle square root function, but you only specify that later, not in the "proof". I was merely trying to point out that you were wrong when you said that for a=a to imply that sqrt(a)=sqrt(a) we need to take the principle square root. There are two possible roots, one where we do have that sqrt(x^y) = x^(y/2)(ie. sqrt(i^4) = i^2)and one where sqrt(1) = 1.
I am not trying to say that you were wrong, obviously the problem is with the sqrt step. It's just that the way you put it seemed misleading, at least to me. What I was trying to say is that it is not necessary to assume that sqrt is the principle square root function. I probably should have written something like "There is actually nothing wrong with taking the general square root of a complex number".
Also, I never said that i^4 is imaginary ;) .
There is actually nothing wrong with taking the square root of a complex number. The problem is that the sqrt(x) can be x or -x. After taking sqrt(i^4) = sqrt(1), you get +/- i^2 = +/- 1.
The recipient sees Cosmetic Carbon Copies (CCCs) as regular CCs, so a Reply-All would be sent to everyone. Oops.
"Man those slashdotters were so stupid to trust their personal comments and entertainment to a site that might some day switch to the color pink! Haha, what a bunch of fools!"
You clearly weren't here on April Fool's Day. OMG PONIES!!!