Question

\[x={-1 \over x}\]

Answer 1

x= i

Answer 2

multiplying by \(x\) on both sides, \(x^2 = -1\) so be definition, \(x=i=\sqrt{-1}\)

Answer 3

so where does the negative sign go?

Answer 4

By definition, \(\sqrt{-1} = i\) and \(i^2 = -1\)

Answer 5

\[\sqrt{-1}={-1 \over \sqrt{-1}}\]

Answer 6

Yes, it's definitive that -√(i)=i^-1, I thought.

Answer 7

the negative comes from the index?.

Answer 8

i^n=i^nmod(4)