[eli5] Why is imaginary number root -1? Why not root -n, since no number times each other would result in negative number?
In: Mathematics
Because the purpose for imaginary numbers is that you can calculate with them in the same way as with real numbers. If i was just an abstract element sqrt(-n) then sqrt(-1) would be i but sqrt(-4) would also be i. But then we have i=sqrt(-4)=sqrt(4)*sqrt(-1)=2*i. This is only possible if i=0 and the whole thing falls apart.
Or to make a more simple argument, if i=sqrt(-n) then what is i² ? It’d have to be undefined and what use is an imaginary number if you can’t even square it?
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