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 a≥0.
It is said that even Euler got confused with √ab=√a√b. Or did he? See Euler's "mistake''? The radical product rule in historical perspective (Amer. Math. Monthly 114 (2007), no. 4, 273–285).
No comments:
Post a Comment