Friday, 22 December 2017

algebra precalculus - Why sqrt1times1neqsqrt12?




We know i2=1then why does this happen?
i2=1×1
=1×1

=1
=1



EDIT: I see this has been dealt with before but at least with this answer I'm not making the fundamental mistake of assuming an incorrect definition of i2.


Answer



From i2=1 you cannot conclude that i=1, just like from (2)2=4 you cannot conclude that 2=4. The symbol a is by definition the positive square root of a and is only defined for a0.




It is said that even Euler got confused with ab=ab. Or did he? See Euler's "mistake''? The radical product rule in historical perspective (Amer. Math. Monthly 114 (2007), no. 4, 273–285).


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