#### What is wrong with this calculation?

Here are 2 ways of computing: \frac{1}{i} leading to different results. Which one is correct and why?

**Method 1**: \frac{1}{i}=\frac{i^4}{i}=i^3=i^2.i=-i

**Method 2**: \frac{1}{i}=\frac{1}{\sqrt{-1}}=\sqrt{\frac{1}{-1}}=\sqrt{\frac{\left(-1\right)^2}{-1}}=\sqrt{-1}=i

I cannot figure out which of the methods gives the correct answer and what's wrong with the incorrect method.