Friday, 22 November 2013

fake proofs - Why is i3 (the complex number "i") equal to i instead of i?




i3=iii=111=(1)(1)(1)=1=i



Please take a look at the equation above. What am I doing wrong to understand i3=i, not i?


Answer



We cannot say that ab=ab for negative a and b. If this were true, then 1=1=(1)(1)=11=ii=1. Since this is false, we have to say that abab in general when we extend it to accept negative numbers.


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