- #1

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[tex]-4 = -4[/tex]

[tex]\frac{-4}{1} = \frac{4}{-1}[/tex]

[tex]\sqrt{\frac{-4}{1}} = \sqrt{\frac{4}{-1}}[/tex]

[tex]\frac{\sqrt{-4}}{1} = \frac{\sqrt{4}}{\sqrt{-1}}[/tex]

[tex]\frac{\sqrt{-1}\sqrt{4}}{1} = \frac{\sqrt{4}}{\sqrt{-1}}[/tex]

[tex]\frac{2i}{1} = \frac{2}{i}[/tex]

[tex]2i^2 = 2[/tex]

[tex]-2 = 2[/tex]

It's clear that the equality [itex]\frac{2i}{1} = \frac{2}{i}[/itex] is wrong because on the LHS we have a complex number (of the form a + ib) but the RHS is not. But the real flaw is probably higher. Any idea?