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what's wrong with the following proof:

[tex]i = \sqrt\left(-1\right)[/tex]

[tex]i.i = \sqrt{\left(-1\right)}.\sqrt{\left(-1\right)}[/tex]

[tex]i^2 = \sqrt\left(-1\right).\left(-1\right)[/tex]

[tex]i^2 = \sqrt 1[/tex]

[tex]i^2 = 1[/tex]

but we know that i

[tex]i = \sqrt\left(-1\right)[/tex]

[tex]i.i = \sqrt{\left(-1\right)}.\sqrt{\left(-1\right)}[/tex]

[tex]i^2 = \sqrt\left(-1\right).\left(-1\right)[/tex]

[tex]i^2 = \sqrt 1[/tex]

[tex]i^2 = 1[/tex]

but we know that i

^{2}= -1
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