complex numbers - 1 = -1 Clearest way to explain why this proof is wrong.

Say you are a high school student or a young undergrad. You are being taught about complex numbers and you are told that $i = \sqrt{-1}$.

You go home and you write this:
\begin{equation}
\begin{aligned}
1 & = 1 \\
1 & = \sqrt{1} \\
1 & = \sqrt{(-1)(-1)} \\
1 & = \sqrt{-1}\sqrt{-1} \\
1 & = i \times i \\
1 & = i^2 \\

1 & = -1
\end{aligned}
\end{equation}

You are dismayed. The infamous imaginary numbers are inconsistent after all!

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The best answer would be the clearest explanation of why the "proof" is faulty, keeping in mind the level of the student. An explanation is extra clear if t presents insights to the student, as well as being correct and concise.