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−1=i…(1)1−1=1i…(2)1−1=1i…(3)1−1=1i…(4)−11=1i…(5)−11=1i…(6)i=1i…(7)i2=1…(8)−1=1…(9)\begin{aligned} \sqrt{-1}=&i \quad&\ldots(1) \\ \dfrac{1}{\sqrt{-1}}=&\dfrac{1}{i}\quad& \ldots(2) \\ \dfrac{\sqrt {1}}{\sqrt{-1}}=&\dfrac{1}{i} \quad &\ldots(3) \\ \sqrt{\dfrac{1}{-1}}=&\dfrac{1}{i} \quad &\ldots(4) \\ \sqrt{\dfrac{-1}{1}}=&\dfrac{1}{i}\quad &\ldots(5) \\ \dfrac{\sqrt{-1}}{1}=&\dfrac{1}{i} \quad &\ldots(6) \\ i=&\dfrac{1}{i} \quad& \ldots(7) \\ i^2=&1 \quad & \ldots (8) \\ -1=&1\quad & \ldots(9) \end{aligned}−1=−11=−11=−11=1−1=1−1=i=i2=−1=ii1i1i1i1i1i111…(1)…(2)…(3)…(4)…(5)…(6)…(7)…(8)…(9)
Consider these steps above.
In which step is the (first) mistake committed?
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