Just want too make sure I am right

Sqrt(-1) = i

i^2 =sqrt(-1) x sqrt(-1) = - 1 (you got it right)

i^3 = -1 x i = -i

i^4 =-1 x -1 = 1 Then the pattern repeats.

Yup correct.

\(\sqrt{-1}=i\)

\(i \times i = \sqrt{-1} \times \sqrt{-1} = {\sqrt{-1}}^{2} = -1\)

yes.