I came across something the other day involving complex numbers.

It is obvious that: \( \frac {1}{ -1} = -1 = \frac {-1}{1} \).

If we take square roots on both sides, we get: \( \frac {1}{i} = \frac {i} {1} \).

Multiplying gives \( 1 = 1 \times 1 = i \times i = -1 \).

So, \(1 = -1\)?

I don't understand what is wrong. Can someone help?